{"title":"Ergebnisse Der Mathematik Und Ihrer Grenzgebiete 2 Folge","description":null,"products":[{"product_id":"symmetric-bilinear-forms-book-john-milnor-9783642883323","title":"Symmetric Bilinear Forms","description":"The theory cf quadratic forms and the intimately related theory of sym- metrie bilinear forms have a lang and rich his tory, highlighted by the work of Legendre, Gauss, Minkowski, and Hasse. (Compare [Dickson] and [Bourbaki, 24, p. 185].) Our exposition will concentrate on the rela- tively recent developments which begin with and are inspired by Witt's 1937 paper \"Theorie der quadratischen Formen in beliebigen Korpern.\" We will be particularly interested in the work of A. Pfister and M. Knebusch. However, some older material will be described, particularly in Chapter II. The presentation is based on lectures by Milnor at the Institute for Ad- vanced Study, and at Haverford College under the Phillips Lecture Pro- gram, during the Fall of 1970, as weIl as Iectures at Princeton University il1 1966. We want to thank J. Cunningham, M. Knebusch, M. Kneser, A. Rosenberg, W. Scharlau and J.-P. Serre for helpful suggestions and corrections. Prerequisites. The reader should be familiar with the rudiments of algebra., incJuding for example the concept of tensor product for mo- dules over a commutative ring. A few individual sections will require quite a bit more. The logical relationship between the various chapters can be roughly described by the diagram below. There are also five appendices, largely self-contained, which treat special topics. I. Arbitrary commutative rings I H. The ring of V. Miscellaneous IIl. Fields integers examples IV. Dedekind domains Contents Chapter r. Basie Coneepts ...","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":50684566470929,"sku":"","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":50684566569233,"sku":"GOR014035515","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52671975751953,"sku":"NLS9783642883323","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/364288332X.jpg?v=1751031785"},{"product_id":"first-order-logic-book-raymond-r-smullyan-9783642867200","title":"First-Order Logic","description":"Except for this preface, this study is completely self-contained. It is intended to serve both as an introduction to Quantification Theory and as an exposition of new results and techniques in \"analytic\" or \"cut-free\" methods. We use the term \"analytic\" to apply to any proof procedure which obeys the subformula principle (we think of such a procedure as \"analysing\" the formula into its successive components). Gentzen cut-free systems are perhaps the best known example of ana­ lytic proof procedures. Natural deduction systems, though not usually analytic, can be made so (as we demonstrated in [3]). In this study, we emphasize the tableau point of view, since we are struck by its simplicity and mathematical elegance. Chapter I is completely introductory. We begin with preliminary material on trees (necessary for the tableau method), and then treat the basic syntactic and semantic fundamentals of propositional logic. We use the term \"Boolean valuation\" to mean any assignment of truth values to all formulas which satisfies the usual truth-table conditions for the logical connectives. Given an assignment of truth-values to all propositional variables, the truth-values of all other formulas under this assignment is usually defined by an inductive procedure. We indicate in Chapter I how this inductive definition can be made explicit-to this end we find useful the notion of a formation tree (which we discuss earlier).","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51061139341585,"sku":"","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51061141635345,"sku":"NIN9783642867200","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52655851831569,"sku":"NLS9783642867200","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3642867200.jpg?v=1750774641"},{"product_id":"sums-of-independent-random-variables-book-vv-petrov-9783642658112","title":"Sums of Independent Random Variables","description":"The classic \"Limit Dislribntions fOT slt1ns of Independent Ramdorn Vari- ables\" by B. V. Gnedenko and A. N. Kolmogorov was published in 1949. Since then the theory of summation of independent variables has devel- oped rapidly. Today a summing-up of the studies in this area, and their results, would require many volumes. The monograph by I. A. Ibragi- mov and Yu. V. I~innik, \"Independent and Stationarily Connected VaTiables\", which appeared in 1965, contains an exposition of the contem- porary state of the theory of the summation of independent identically distributed random variables. The present book borders on that of Ibragimov and Linnik, sharing only a few common areas. Its main focus is on sums of independent but not necessarily identically distri- buted random variables. It nevertheless includes a number of the most recent results relating to sums of independent and identically distributed variables. Together with limit theorems, it presents many probahilistic inequalities for sums of an arbitrary number of independent variables. The last two chapters deal with the laws of large numbers and the law of the iterated logarithm. These questions were not treated in Ibragimov and Linnik; Gnedenko and KolmogoTOv deals only with theorems on the weak law of large numbers. Thus this book may be taken as complementary to the book by Ibragimov and Linnik. I do not, however, assume that the reader is familiar with the latter, nor with the monograph by Gnedenko and Kolmogorov, which has long since become a bibliographical rarity.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51062903111953,"sku":"","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51062906355985,"sku":"NIN9783642658112","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52622548074769,"sku":"NLS9783642658112","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3642658113.jpg?v=1751031782"},{"product_id":"embeddings-and-extensions-in-analysis-book-jh-wells-9783642660399","title":"Embeddings and Extensions in Analysis","description":"The object of this book is a presentation of the major results relating to two geometrically inspired problems in analysis. One is that of determining which metric spaces can be isometrically embedded in a Hilbert space or, more generally, P in an L space; the other asks for conditions on a pair of metric spaces which will ensure that every contraction or every Lipschitz-Holder map from a subset of X into Y is extendable to a map of the same type from X into Y. The initial work on isometric embedding was begun by K. Menger [1928] with his metric investigations of Euclidean geometries and continued, in its analytical formulation, by I. J. Schoenberg [1935] in a series of papers of classical elegance. The problem of extending Lipschitz-Holder and contraction maps was first treated by E. J. McShane and M. D. Kirszbraun [1934]. Following a period of relative inactivity, attention was again drawn to these two problems by G. Minty's work on non-linear monotone operators in Hilbert space [1962]; by S. Schonbeck's fundamental work in characterizing those pairs (X,Y) of Banach spaces for which extension of contractions is always possible [1966]; and by the generalization of many of Schoenberg's embedding theorems to the P setting of L spaces by Bretagnolle, Dachuna Castelle and Krivine [1966].","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51063754326289,"sku":"","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51063757766929,"sku":"NIN9783642660399","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52617243918609,"sku":"NLS9783642660399","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3642660398.jpg?v=1750807149"},{"product_id":"littlewood-paley-and-multiplier-theory-book-r-e-edwards-9783642663680","title":"Littlewood-Paley and Multiplier Theory","description":"This book is intended to be a detailed and carefully written account of various versions of the Littlewood-Paley theorem and of some of its applications, together with indications of its general significance in Fourier multiplier theory. We have striven to make the presentation self-contained and unified, and adapted primarily for use by graduate students and established mathematicians who wish to begin studies in these areas: it is certainly not intended for experts in the subject. It has been our experience, and the experience of many of our students and colleagues, that this is an area poorly served by existing books. Their accounts of the subject tend to be either ill-suited to the needs of a beginner, or fragmentary, or, in one or two instances, obscure. We hope that our book will go some way towards filling this gap in the literature. Our presentation of the Littlewood-Paley theorem proceeds along two main lines, the first relating to singular integrals on locally com­ pact groups, and the second to martingales. Both classical and modern versions of the theorem are dealt with, appropriate to the classical n groups IRn, ?L , Tn and to certain classes of disconnected groups. It is for the disconnected groups of Chapters 4 and 5 that we give two separate accounts of the Littlewood-Paley theorem: the first Fourier analytic, and the second probabilistic.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51063817896209,"sku":"","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51063820648721,"sku":"NIN9783642663680","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52655853601041,"sku":"NLS9783642663680","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3642663680.jpg?v=1750870694"},{"product_id":"boolean-algebras-book-roman-sikorski-9783642858222","title":"Boolean Algebras","description":"There are two aspects to the theory of Boolean algebras; the algebraic and the set-theoretical. A Boolean algebra can be considered as a special kind of algebraic ring, or as a generalization of the set-theoretical notion of a field of sets. Fundamental theorems in both of these directions are due to M. H. STONE, whose papers have opened a new era in the develop­ ment of this theory. This work treats the set-theoretical aspect, with little mention being made of the algebraic one. The book is composed of two chapters and an appendix. Chapter I is devoted to the study of Boolean algebras from the point of view of finite Boolean operations only; a greater part of its contents can be found in the books of BIRKHOFF [2J and HERMES [1]. Chapter II seems to be the first systematic study of Boolean algebras with infinite Boolean operations. To understand Chapters I and II it suffices only to know fundamental notions from general set theory and set-theoretical topology. No know­ ledge of lattice theory or of abstract algebra is presumed. Less familiar topological theorems are recalled, and only a few examples use more advanced topological means; but these may be omitted. All theorems in both chapters are given with full proofs.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51065112101137,"sku":"","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51065113805073,"sku":"NIN9783642858222","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52429390315793,"sku":"NLS9783642858222","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3642858228.jpg?v=1751000291"},{"product_id":"la-geometrie-des-groupes-classiques-book-jean-dieudonne-9783540029670","title":"La geometrie des groupes classiques","description":"This book gives an excellent survey of recent work on classical groups, simplifying and unifying the results of many authors. No attempt is made to cover all of the voluminous literature on classical groups; the author deals with only that portion of the subject which can be handled by the methods of linear algebra. By thus restricting his scope, he is able to include proofs of most of the results described, thereby making the book more self-contained than most Ergebnisse tracts.  In the reviewer's opinion, this is an important and well-written book which should help to stimulate research on the classical groups. The book not only gives a thorough exposition of the present state of the subject, but is also an excellent introduction to the modern techniques basic to further work in this field.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51066961199377,"sku":"","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51066963493137,"sku":"NIN9783540029670","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52591012970769,"sku":"NLS9783540029670","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3540029672.jpg?v=1751127213"},{"product_id":"geometric-invariant-theory-book-david-mumford-qc-9783540569633","title":"Geometric Invariant Theory","description":"“Geometric Invariant Theory” by Mumford\/Fogarty (the first edition was published in 1965, a second, enlarged edition appeared in 1982) is the standard reference on applications of invariant theory to the construction of moduli spaces. This third, revised edition has been long awaited for by the mathematical community. It is now appearing in a completely updated and enlarged version with an additional chapter on the moment map by Prof. Frances Kirwan (Oxford) and a fully updated bibliography of work in this area. The book deals firstly with actions of algebraic groups on algebraic varieties, separating orbits by invariants and construction quotient spaces; and secondly with applications of this theory to the construction of moduli spaces. It is a systematic exposition of the geometric aspects of the classical theory of polynomial invariants.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51423581438225,"sku":"","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ GOOD \/ SBYB","offer_id":51423582617873,"sku":"CIN3540569634G","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3540569634.jpg?v=1780739083"},{"product_id":"manifolds-all-of-whose-geodesics-are-closed-book-a-l-besse-9783540081586","title":"Manifolds all of whose Geodesics are Closed","description":"X 1 O S R Cher lecteur, J'entre bien tard dans la sphere etroite des ecrivains au double alphabet, moi qui, il y a plus de quarante ans deja, avais accueilli sur mes terres un general epris de mathematiques. JI m'avait parle de ses projets grandioses en promettant d'ailleurs de m'envoyer ses ouvrages de geometrie. Je suis entiche de geometrie et c'est d'elle dontje voudrais vous parler, oh  certes pas de toute la geometrie, mais de celle que fait l'artisan qui taille, burine, amene, gauchit, peaufine les formes. Mon interet pour le probleme dont je veux vous entretenir ici, je le dois a un ami ebeniste. En effet comme je rendais un jour visite il cet ami, je le trouvai dans son atelier affaire a un tour. Il se retourna bientot, puis, rayonnant, me tendit une sorte de toupie et me dit: Monsieur Besse, vous qui calculez les formes avec vos grimoires, que pensez-vous de ceci?)) Je le regardai interloque. Il poursuivit: Regardez  Si vous prenez ce collier de laine et si vous le maintenez fermement avec un doigt place n'importe ou sur la toupie, eh bien  la toupie passera toujours juste en son interieur, sans laisser le moindre espace.)) Je rentrai chez moi, fort etonne, car sa toupie etait loin d'etre une boule. Je me mis alors au travail .","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52127632392465,"sku":"NLS9783540081586","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ GOOD \/ SBYB","offer_id":52851994001681,"sku":"CIN3540081585G","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540081586.jpg?v=1757487341"},{"product_id":"infinite-linear-groups-book-bertram-wehrfritz-9783642870835","title":"Infinite Linear Groups","description":"By a linear group we mean essentially a group of invertible matrices with entries in some commutative field. A phenomenon of the last twenty years or so has been the increasing use of properties of infinite linear groups in the theory of (abstract) groups, although the story of infinite linear groups as such goes back to the early years of this century with the work of Burnside and Schur particularly. Infinite linear groups arise in group theory in a number of contexts. One of the most common is via the automorphism groups of certain types of abelian groups, such as free abelian groups of finite rank, torsion-free abelian groups of finite rank and divisible abelian p-groups of finite rank. Following pioneering work of Mal'cev many authors have studied soluble groups satisfying various rank restrictions and their automor- phism groups in this way, and properties of infinite linear groups now play the central role in the theory of these groups. It has recently been realized that the automorphism groups of certain finitely generated soluble (in particular finitely generated metabelian) groups contain significant factors isomorphic to groups of automorphisms of finitely generated modules over certain commutative Noetherian rings. The results of our Chapter 13, which studies such groups of automorphisms, can be used to give much information here.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52135880950033,"sku":"NLS9783642870835","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642870835.jpg?v=1757551406"},{"product_id":"inequalities-book-edwin-f-beckenbach-9783642649738","title":"Inequalities","description":"Since the elassie work on inequalities by HARDY, LITTLEWOOD, and P6LYA in 1934, an enonnous amount of effort has been devoted to the sharpening and extension of the elassieal inequalities, to the discovery of new types of inequalities, and to the application of inqualities in many parts of analysis. As examples, let us eite the fields of ordinary and partial differential equations, whieh are dominated by inequalities and variational prineiples involving functions and their derivatives; the many applications of linear inequalities to game theory and mathe- matieal economics, which have triggered a renewed interest in con- vexity and moment-space theory; and the growing uses of digital com- puters, which have given impetus to a systematie study of error esti- mates involving much sophisticated matrix theory and operator theory. The results presented in the following pages reflect to some extent these ramifications of inequalities into contiguous regions of analysis, but to a greater extent our concem is with inequalities in their native habitat. Since it is elearly impossible to give a connected account of the burst of analytic activity of the last twenty-five years centering about inequalities, we have d. eeided to limit our attention to those topies that have particularly delighted and intrigued us, and to the study of whieh we have contributed.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52136734621969,"sku":"NLS9783642649738","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642649738.jpg?v=1757554768"},{"product_id":"theorie-der-funktionen-mehrerer-komplexer-veranderlichen-book-w-barth-9783540050865","title":"Theorie der Funktionen mehrerer komplexer Veränderlichen","description":null,"brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52139546640657,"sku":"NLS9783540050865","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":53494285795601,"sku":"NIN9783540050865","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540050865.jpg?v=1757569608"},{"product_id":"additive-zahlentheorie-book-hans-h-ostmann-9783662008430","title":"Additive Zahlentheorie","description":"Der hier vorliegende Bericht ist der zweite Teil des Ergebnisberichtes uber additive Zahlentheorie und behandelt, wie schon im Vorwort des ersten Teils erwahnt, spezielle Mengen nichtnegativer ganzer Zahlen. Fur die Untersuchung solcher Mengen genugt zumeist schon die Kennt- nis gewisser Struktureigenschaften, so da die gewonnenen Resultate in der Regel gleich fur ganze Klassen von Mengen Gultigkeit haben. Dieser Gesichtspunkt ist namentlich fur die Abschnitte 18, 19 und 20 magebend. - Entsprechend der Entwicklung allgemeiner Begriffs- bildungen und Satze innerhalb der additiven Zahlentheorie, wie der Dichtentheorie, der Theorie der Basismengen usw., interessiert natur- gema die Kenntnis der diesbezuglichen wesentlichen Groen bei speziellen Mengen. Insbesondere ordnet sich diesem Gesichtspunkt ohne weiteres auch die Aufgabe unter, die charakteristischen","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52140379701521,"sku":"NLS9783662008430","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783662008430.jpg?v=1757574216"},{"product_id":"topics-in-the-theory-of-lifting-book-alexandra-ionescu-tulcea-9783642885099","title":"Topics in the Theory of Lifting","description":"The problem as to whether or not there exists a lifting of the M't\/. 1 space ) corresponding to the real line and Lebesgue measure on it was first raised by A. Haar. It was solved in a paper published in 1931 [102] by 1. von Neumann, who established the existence of a lifting in this case. In subsequent papers J. von Neumann and M. H. Stone [105], and later on 1. Dieudonne [22], discussed various algebraic aspects and generalizations of the problem. Attemps to solve the problem as to whether or not there exists a lifting for an arbitrary M't\/. space were unsuccessful for a long time, although the problem had significant connections with other branches of mathematics. Finally, in a paper published in 1958 [88], D. Maharam established, by a delicate argument, that a lifting of M't\/. always exists (for an arbi­ trary space of a-finite mass). D. Maharam proved first the existence of a lifting of the M't\/. space corresponding to a product X = TI {ai,b,} ieI and a product measure J.1= Q9 J.1i' with J.1i{a;}=J.1i{b,}=! for all iE\/. ,eI Then, she reduced the general case to this one, via an isomorphism theorem concerning homogeneous measure algebras [87], [88]. A different and more direct proof of the existence of a lifting was subsequently given by the authors in [65]' A variant of this proof is presented in chapter 4.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52140899205393,"sku":"NLS9783642885099","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642885099.jpg?v=1757576061"},{"product_id":"neuere-methoden-und-ergebnisse-der-ergodentheorie-book-konrad-jacobs-9783540025177","title":"Neuere Methoden und Ergebnisse der Ergodentheorie","description":"Seit dem Erscheinen des berfihmten Ergebnisberichts von E. HOPF [9] (1937) ist eine umfangreiche Literatur fiber ergodentheoretische Fragen entstanden. Die vorliegende Arbeit ist ein Versuch, in diese Literatur ein­ zuffihren und die wesentlichsten Ergebnisse geschlossen darzustellen. Zusammenfassende Darstellungen einzelner Fragenkreise sind bereits frfiher in den Arbeiten von DUNFORD-SCHWARTZ [1], HALMOS [9], [to], KAKUTANI [11] und OXTOBY [3], [4] gegeben worden. Ichhabe michstark auf sie gestfitzt. Als Einffihrung und Uberblick ist das reizvolle Bfichlein von HALMOS [to] sehr zu empfehlen. Bei der Sichtung des Materials schien es mir zweckmaBig, zwei Teil­ gebiete von vornherein auszuscheiden: 1. Die rein topologischen Unter­ suchungen; sie sind in dem Buch von GOTTSCHALK-HEDLUND [3] syste­ matisch entwickelt; ich habe lediglich in Kap. 5 § 1 eine kleine Kostprobe eingeffigt. 2. Die Untersuchungen fiber geodatische Stromungen; hieruber gibt es systematische Darstellungen bei HOPF [9], [to] und GOTTSCHALK­ HEDLUND [3]. Das Literaturverzeichnis umfaBt gleichwohl auch diese beiden Disziplinen; ich habe versucht, es so vollstandig wie moglich zu machen. Es enthalt daher auch Arbeiten, die im Text nicht zitiert werden. - Ferner habe ich alle spektral-theoretischen Untersuchungen beiseitegelassen (vgl. HOPF [9], auch HALMOS [to]) undstattdessen Unter­ suchungen fiber Fastperiodizitat ausfUhrlicher behandelt (Kap. 1, § 6 und 7). - DooB [9] und KAKUTANI [11] haben Analogien zwischen dem individuellen Ergodensatz und dem bekannten Satz fiber die Fastfiberall­ konvergenz von Martingalen hervorgehoben. In Kap.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52141415235857,"sku":"NLS9783540025177","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540025177.jpg?v=1757577115"},{"product_id":"additive-zahlentheorie-book-hans-h-ostmann-9783662110317","title":"Additive Zahlentheorie","description":"Bereits seit l ngerer Zeit hat sich die additive Zahlentheorie als gesonderter Zweig innerhalb der Zahlentheorie herausgebildet; aber erst in den letzten Jahrzehnten hat dieses Gebiet neue Antriebe erhalten. In der klassischen additiven Zahlentheorie waren die Untersuchungs- objekte im wesentlichen solche Fragestellungen, die an ganz spezielle Zahlenmengen gekn pft sind, wie etwa das GOLDBAcHsche oder das WARINGSche Problem. Diese bei den Probleme waren es aber auch, die den Ansto  zu einer neuen Entwicklung in der additiven Zahlentheorie gaben, als 1930 SCHNIRELMANN in seiner fundamentalen Arbeit  ber additive Eigenschaften von Zahlen  lJ einen neuen Zugang zu den ge- nannten Problemen fand. SCHNIRELMANN entwickelte n mlich zun chst eine Theorie, die ganz von der speziellen Natur der Primzahlen bzw. der k-ten Potenzen absah und sich allgemein auf Mengen nat rlicher Zahlen bezog. Jeder solchen Menge wird eine reelle Zahl, die Dichte zuge- ordnet, die in gewissem Sinn ein Ma  daf r ist, welcher Anteil aus der Gesamtheit aller nat rlichen Zahlen der gegebenen Menge angeh rt. An Stelle der arithmetischen Natur der Zahlenmenge tritt also ein in dieser Weise zu verstehender metrischer Gesichtspunkt. Indem ferner noch die Summe solcher Mengen eingef hrt wurde, zeigte sich, da  bereits in gro er Allgemeinheit wesentliche Aussagen gemacht werden konnten. 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DaB aber bei einer ersten derartigen Darstellung verschiedene Schwierigkeiten zu fiberwinden sind, nicht zuletzt auch in rein didakti­ scher Hinsicht, stellt sich wahrend der Bearbeitung eines solchen Stoffes Ofters heraus. So hat es sich unter anderem a1s recht heikel erwiesen, schon nur die verschiedenen Definitionen, welche fiber quasikonforme Abbildungen existieren, auf einen einigermaBen gleichen Nenner zu bringen. Da neben einer russischen Darstellung (VOLKOVYSKIJ [2]) fiber das vorliegende Forschungsgebiet noch keinerlei Lehrbficher existieren, habe ich besonders Wert darauf gelegt, an einigen Stellen etwas tiefer in die Beweisverfahren einzudringen, als dies ublicherweise in der vorliegenden Reihe der Ergebnishefte der Fall ist. In verdankenswerter Weise hat mir Herr A. TEBLING verschiedene russische Arbeiten ins Deutsche ubersetzt, wodurch es mir ermoglicht wurde, auch die sonst nur schwer zugangliche russische Literatur zu berucksichtigen. 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An erster Stelle danke ich meinen Lehrern der Funktionentheorie, den Herren Professoren R.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52426825498897,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52426825957649,"sku":"NLS9783540025153","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540025153.jpg?v=1759159083"},{"product_id":"geometric-invariant-theory-book-david-mumford-qc-9783642634000","title":"Geometric Invariant Theory","description":"This standard reference on applications of invariant theory to the construction of moduli spaces is a systematic exposition of the geometric aspects of classical theory of polynomial invariants. 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Subsequent important contributions before 1940 were made by SEIDEL [1-2J, DOOE [1-4J, CARTWRIGHT [1-3J and BEURLING [1]. The investigations of SEIDEL and BEURLING gave great impetus and interest to Japanese mathematicians; beginning about 1940 some contributions were made to the theory by KUNUGUI [1-3J, IRIE [IJ, TOKI [IJ, TUMURA [1-2J, KAMETANI [1-4J, TsuJI [4J and NOSHIRO [1-4J. Recently, many noteworthy advances have been made by BAGEMIHL, SEIDEL, COLLINGWOOD, CARTWRIGHT, HERVE, LEHTO, LOHWATER, MEIER, OHTSUKA and many other mathematicians. The main purpose of this small book is to give a systematic account on the theory of cluster sets. Chapter I is devoted to some definitions and preliminary discussions. 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HIGMAN for their kindness in giving hirn many valuable suggestions. His thanks are also due to Dr. NOBORU ITo who, during stimulating conversations, contributed many useful ideas. Urbana, May, 1956. M. Suzuki. Contents.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52426983801105,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52426984587537,"sku":"NLS9783642527609","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642527609.jpg?v=1759159589"},{"product_id":"derivation-and-martingales-book-charles-a-hayes-9783642861826","title":"Derivation and Martingales","description":"In Part I of this report the pointwise derivation of scalar set functions is investigated, first along the lines of R. DE POSEL (abstract derivation basis) and A. P. MORSE (blankets); later certain concrete situations (e. g., the interval basis) are studied. 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LJAPUNOV (1857 bis 1918) uber die Stabilitat der Bewegung, die 1892 in russischer Sprache, 1907 in franzosischer Ubersetzung  erschien, hat ursprunglich nur wenig Beach- tung gefunden und war lange Zeit hindurch nahezu vergessen. Erst vor etwa 25 Jahren wurden diese Untersuchungen von einigen sowjetischen Mathematikern wieder aufgegriffen. Man bemerkte dabei, da sich die Ljapunovschen Ansatze zur Bewaltigung konkreter Probleme der Physik und Technik eigneten, und seitdem befat man sich, wie die wachsende Zahl der Veroffentlichungen erkennen lat, in steigendem Mae mit der von LJAPUNOV begrundeten Stabilitatstheorie. Vor allem gilt das fur die sogenannte zweite oder direkte Methode. LJAPUNOV hat sie eigentlich nur zur Ableitung von Stabilitatskriterien der theoretischen Mechanik benutzt. Jetzt verwendet man sie einerseits bei praktischen Aufgaben aus dem Bereich der mechanischen und elektrischen Schwin- gungen, insbesondere in der Regelungstechnik; andererseits hat man erkannt, da die direkte Methode als leitendes Prinzip einer allgemeinen Stabilitatstheorie dienen kann, die erheblich mehr umfat als die bei gewohnlichen Differentialgleichungen auftretenden Probleme. Die Theorie der direkten Methode ist in den letzten Jahren sehr gefordert und zu einem gewissen Abschlu gebracht worden. Sie kann daher jetzt in einem zusammenfassenden Ergebnisbericht dargestellt werden. Eine Ubersicht, die diese Dinge einem groeren Kreise naher- bringen kann, erscheint um so mehr angezeigt, als fast die gesamte Literatur in russischer Sprache und an teilweise schwer zuganglichen Stellen erschienen isP.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52427587846417,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52427588534545,"sku":"NLS9783642527708","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642527708.jpg?v=1759161441"},{"product_id":"knotentheorie-book-k-reidemeister-9783540062974","title":"Knotentheorie","description":"Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. 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Den  quivalenzen zum Auswahlaxiom (  31) und zur Alephhypothese (  35) sowie den un- erreichbaren Zahlen (  40-42) wird besondere Beachtung geschenkt. Auf das Problem der formalen Darstellung von Ordnungszahlen, auf Anwen- dungen der transfiniten Zahlen in der Theorie der Punktmengen und andere Anwendungen konnte wegen des beschr nkten zur Verf gung stehenden Raumes nicht stark eingegangen werden. Am Schlu  findet sich ein Literaturverzeichnis, in dem die modemen Arbeiten fast voll- st ndig, die  lteren nur teilweise aufgef hrt sind, sowie ein Sachver- zeichnis. F r wertvolle Ratschl ge m chte ich den Herren Prof. Dr. P. FINSLER, P. -D. Dr. W. NEUMER, Prof. Dr. P. BERNAYS, Dr. G. M LLER und besonders Prof. Dr. E. SPECKER meinen herzlichsten Dank aussprechen. Z rich, im Januar 1955 HEINZ BACHMANN Eidg. Sternwarte, Z rich Inhaltsverzeichnis Seite J. Einleitung: Allgemeine mengentheoretis6he Vorbemerkungen 1   1. Mengenlehre und Grundlagenproblem . . . . . . . . . . . . . . . . . . . . . . . . 1   2. Die  blichen Axiome der Mengenlehre . . . . . . . . . . . . . . . . . . . . . . . 6   3. Einf hrung der transfiniten Zahlen . . . . . . . . . . . . . . . . . . . . . . . . . . 13 U. Ordnungszahlen und transfinite Funktionen . . . . . . . . . . . . . . . . . . . . . 19   4. Die Ordnungszahlen . . . . . . . . . . . . . . . . . . -. . . . . . . . . . . . . . . . . . . . . 19   5. Stetige Funktionen von Ordnungszahlen . . . . . . . . . . . . . . . . . . . . . 28 33 38 40 45 Berichtigungen 49 xEX S. 28. 15.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52428003508497,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52428004098321,"sku":"NLS9783642885150","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642885150.jpg?v=1759162794"},{"product_id":"finite-sections-of-some-classical-inequalities-book-herbert-s-wilf-9783642867149","title":"Finite Sections of Some Classical Inequalities","description":"Hardy, Littlewood and P6lya's famous monograph on inequalities [17J has served as an introduction to hard analysis for many mathema­ ticians. Some of its most interesting results center around Hilbert's inequality and generalizations. 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This viewpoint leads to the exclusion of some material which might belong to a broader-based discussion, such as the elegant work of Baxter, Hirschman and others on the strong Szego limit theorem, and the inclusion of other work, such as that of de Bruijn and his students, which is basically nonlinear, and is therefore in some sense disjoint from the earlier investigations. I am grateful to Professor Halmos for inviting me to prepare this volume, and to Professors John and Olga Todd for several helpful comments. Philadelphia, Pa. 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Deutsche Akademie der vVissenschaften zu Berlin Institut fur Reine Mathematik Albrecht Pietsch Foreword to the Second Edition Since the appearance of the first edition, some important advances have taken place in the theory of nuclear locally convex spaces. Firsts there is the Universality Theorem ofT. and Y. Komura which fully confirms a conjecture of Grothendieck. Also, of particular interest are some new existence theorems for bases in special nuclear locally convex spaces. Recently many authors have dealt with nuclear spaces of functions and distributions. Moreover, further classes of operators have been found which take the place of nuclear or absolutely summing operators in the theory of nuclear locally convex spaces. Unfortunately, there seem to be no new results on diametrai or approximative dimension and isomorphism of nuclear locally convex spaces. Since major changes have not been absolutely necessary I have restricted myself to minor additions. Only the tenth chapter has been substantially altered. Since the universality results no longer depend on the existence of a basis it was necessary to introduce an independent eleventh chapter on universal nuclear locally convex spaces. 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Es entstand dann die Frage, ob jede Teilmenge me bar ist. VITALI entdeckte 1905 die Existenz von nicht me baren Teilmengen der Zahlengeraden. Sp ter, als man abstrakte Ma e auf Mengenk rpern bzw. Booleringen (Booleschen Algebren) einf hrte, erhob sich, neben dem Problem der Erweiterung des Definitionsbereiches des abstrakten Ma es, auch die Frage, ob man auf einem beliebigen Mengenk rper bzw. Boolering ein nicht triviales Ma , und zwar mit bestimmten Eigenschaf- ten erkl ren kann. Dies ist im allgemeinen nicht m glich; hier geht wesentlich die Struktur des Mengenk rpers bzw. des Booleringes in das Problem ein. Diese Frage ist f r die Wahrscheinlichkeitstheorie von besonderer Bedeutung, weil man in dies r Theorie die Zufallsereignisse mit abstrakten Mengen oder mit Elementen eines Booleringes darstellt und die Wahrscheinlichkeit als ein normiertes und in gewissen F llen strikt positives Ma  betrachtet.  ber die Strukturtheorie der Wahr- scheinlichkeitsfelder und -r ume sind deshalb in den letzten J ahrzehn- ten viele Untersuchungen angestellt worden. In dem vorliegenden Be- richt haben wir versucht, das Wichtige davon zusammenzustellen. Ein gro er Teil des Berichtes wird den verschiedenen Arten der Unabh n- gigkeit und dem Begriff des cartesischen Produktes gewidmet, Begriffe, die haupts chlich aus Problemen der Wahrscheinlichkeitstheorie ent- standen sind und eine gro e Rolle bei der Charakterisierung der Struktur der Wahrscheinlichkeitsfelder spielen.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52428644778257,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52428645335313,"sku":"NLS9783642527722","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642527722.jpg?v=1759164760"},{"product_id":"surgery-on-simply-connected-manifolds-book-william-browder-9783642500220","title":"Surgery on Simply-Connected Manifolds","description":"This book is an exposition of the technique of surgery on simply-connected smooth manifolds. Systematic study of differentiable manifolds using these ideas was begun by Milnor [45] and Wallace [68] and developed extensively in the last ten years. It is now possible to give a reasonably complete theory of simply-connected manifolds of dimension ~ 5 using this approach and that is what I will try to begin here. The emphasis has been placed on stating and proving the general results necessary to apply this method in various contexts. In Chapter II, these results are stated, and then applications are given to characterizing the homotopy type of differentiable manifolds and classifying manifolds within a given homotopy type. This theory was first extensively developed in Kervaire and Milnor [34] in the case of homotopy spheres, globalized by S. P. Novikov [49] and the author [6] for closed 1-connected manifolds, and extended to the bounded case by Wall [65] and Golo [23]. The thesis of Sullivan [62] reformed the theory in an elegant way in terms of classifying spaces.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52431374975249,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52431375401233,"sku":"NLS9783642500220","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642500220.jpg?v=1759172325"},{"product_id":"topics-in-m-adic-topologies-book-silvio-greco-9783642885037","title":"Topics in m-adic Topologies","description":"The m-adic topologies and, in particular the notions of m-complete ring and m-completion A of a commutative ring A, occur frequently in commutative algebra and are also a useful tool in algebraic geometry. 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In order to emphasize the elementary character of our treatment, we have recalled several well known definitions and, sometimes, even the proofs of the first properties which follow directly from them. 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The Los Angeles ma- script appears. 1970-AN visits JNC at Monash. 1971-The Australian manuscript appears. 1972-JNC visits AN at Cornell. Here is the result. We gratefully acknowledge support from Cornell Vniversity, Vni- versity of California at Los Angeles, Monash Vniversity and National Science Foundation Grants GP 14363, 22719 and 28169. We are deeply indebted to the many people who have helped uso Amongst the mathe- maticians, we are particularly grateful to J. C. E. Dekker, John Myhill, Erik Ellentuck, Peter AczeI, Chris Ash, Charlotte ehell, Ed Eisenberg, Dave Gillam, Bill Gross, Alan Hamilton, Louise Hay, Georg Kreisel, Phil Lavori, Ray Liggett, Al Manaster, Michael D. Morley, Joe Rosen- stein, Graham Sainsbury, Bob Soare and Michael Venning. Last, but by no means least, we thank Anne-Marie Vandenberg, Esther Monroe, Arletta Havlik, Dolores Pendell, and Cathy Stevens and the girls of the Mathematics Department of VCLA in 1968 for hours and hours of excellent typing. Thanksgiving November 1972 J. N. Crossley Ithaca, New Y ork Anil Nerode Contents O. Introduction ...1 Part 1. Categories and Functors 3 1. Categories ...3 2. Morphism Combinatorial Functors 3 3. Combinatorial Functors ...18 Part H. Model Theory . . 18 4. Countable Atomic Models 18 5. Copying . 22 6. Dimension ...26 Part III.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52454612861201,"sku":"NLS9783642859359","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642859359.jpg?v=1759371702"},{"product_id":"mathematische-grundlagenforschung-intuitionismus-beweistheorie-book-a-heyting-9783540062981","title":"Mathematische Grundlagenforschung Intuitionismus Beweistheorie","description":"In den letzten Jahrzehntel  hat sich das Interesse an der Grund- legung der Mathematik immer gesteigert. Fanden frtiher die wenigen Forscher, die sich emsthaft mit dieser 'Frage beschaftigten, wenig Be- achtung, heute ist die Teilnahme sowohl von mathematischer wie von philosophischer Seite fast allgemein. Zu diesem Umschwung hat sieher die CANToRSche Mengenlehre, die gleich nach ihrem Entstehen lebhafte Erorterungen tiber ihre Berechtigung hervorrief, den AnstoB gegeben, und besonders die bei riicksichtsloser Durchfiihrung ihrer Grundgedanken auftretenden Widerspriiche zogen die allgemeine Aufmerksamkeit auf sich. Doch ist die bisweUen noch geauBerte Behauptung, der Zweck -der Grundlagenforschung liege in der Beseitigung der Widersprtiche, verfehlt. In philosophischer und in mathematischer Richtung geht diese weit tiber eine solche Zielsetzung hinaus. Philosophisch untersucht man -das Wesen der mathematischen Erkenntnis, ihre Voraussetzungen und Endziele, ihr Verhaltnis zu anderen Wissensgebieten, insbesondere der Physik, und ihre Abgrenzung gegen diese dem lnhalt und der Methode nacho An diese philosophischen Erorterungen schlieBen sich umfangreiche mathematische Untersuchungen tiber den Aufbau der Mathematik aus den philosophisch gegebenen Voraussetzungen und tiber die Struktur der mathematischen Beweisftihrungen. Einzelne Teilgebiete dieser Unter- suchungen entwickeln sich schon zu selbstandigen Disziplinen, die sich in ihren Methoden und Problemstellungen von der eigentlichen Grund- lagenforschung unabhangig machen; ein Beispiel eines solchen neuen Zweiges der Mathematik, der sein Entstehen der Grundlagenforschung verdankt, ist die mathematischp. Logik. Allmahlich haben sich drei J. auptrichtungen gebildet, die je einer eigenen Auffassung tiber das Wesen der Mathematik entsprechen undo je zu verschieden gearteten mathematischen Untersuchungen geftihrt haben.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52454616334609,"sku":"NLS9783540062981","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540062981.jpg?v=1759371706"},{"product_id":"idealtheorie-book-wolfgang-krull-9783642870347","title":"Idealtheorie","description":"Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfangen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen fur die historische wie auch die disziplingeschichtliche Forschung zur Verfugung, die jeweils im historischen Kontext betrachtet werden mussen. 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