{"title":"R M Dudley","description":null,"products":[{"product_id":"real-analysis-and-probability-book-r-m-dudley-9780521007542","title":"Real Analysis and Probability","description":"This classic textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The first half of the book gives an exposition of real analysis: basic set theory, general topology, measure theory, integration, an introduction to functional analysis in Banach and Hilbert spaces, convex sets and functions and measure on topological spaces. The second half introduces probability based on measure theory, including laws of large numbers, ergodic theorems, the central limit theorem, conditional expectations and martingale's convergence. A chapter on stochastic processes introduces Brownian motion and the Brownian bridge. The edition has been made even more self-contained than before; it now includes a foundation of the real number system and the Stone-Weierstrass theorem on uniform approximation in algebras of functions. Several other sections have been revised and improved, and the comprehensive historical notes have been further amplified. A number of new exercises have been added, together with hints for solution.","brand":"WoB","offers":[{"title":"US \/ WELL_READ \/ SBYB","offer_id":50331561656593,"sku":"CIN0521007542A","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ GOOD \/ INTERNAL","offer_id":50455892623633,"sku":"GOR013959266","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":50457428754705,"sku":"GOR007946572","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51002963755281,"sku":"NIN9780521007542","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ GOOD \/ SBYB","offer_id":52091384332561,"sku":"CIN0521007542G","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52454301171985,"sku":"NLS9780521007542","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0521007542.jpg?v=1751326046"},{"product_id":"real-analysis-and-probability-book-r-m-dudley-9780534100506","title":"Real Analysis and Probability","description":"Written by one of the best-known probabilists in the world this text offers a clear and modern presentation of modern probability theory and an exposition of the interplay between the properties of metric spaces and those of probability measures. This text is the first at this level to include discussions of the subadditive ergodic theorems, metrics for convergence in laws and the Borel isomorphism theory. The proofs for the theorems are consistently brief and clear and each chapter concludes with a set of historical notes and references. This book should be of interest to students taking degree courses in real analysis and\/or probability theory.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51457681096977,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":51457681424657,"sku":"GOR009095852","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0534100503.jpg?v=1750879863"},{"product_id":"differentiability-of-six-operators-on-nonsmooth-functions-and-p-variation-book-r-m-dudley-9783540659754","title":"Differentiability of Six Operators on Nonsmooth Functions and p-Variation","description":"The book is about differentiability of six operators on functions or pairs of functions: composition (f of g), integration (of f dg), multiplication and convolution of two functions, both varying, and the product integral and inverse operators for one function. The operators are differentiable with respect to p-variation norms with optimal remainder bounds. Thus the functions as arguments of the operators can be nonsmooth, possibly discontinuous, but four of the six operators turn out to be analytic (holomorphic) for some p-variation norms. The reader will need to know basic real analysis, including Riemann and Lebesgue integration. The book is intended for analysts, statisticians and probabilists. Analysts and statisticians have each studied the differentiability of some of the operators from different viewpoints, and this volume seeks to unify and expand their results.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52136947974417,"sku":"NLS9783540659754","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540659754.jpg?v=1757555863"},{"product_id":"ecole-d-ete-de-probabilites-de-saint-flour-xii-1982-book-r-m-dudley-9783540138976","title":"Ecole d'Ete de Probabilites de Saint-Flour XII, 1982","description":null,"brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52138580148497,"sku":"NLS9783540138976","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52761645121809,"sku":"NIN9783540138976","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540138976.jpg?v=1757563727"},{"product_id":"real-analysis-and-probability-book-r-m-dudley-9780521809726","title":"Real Analysis and Probability","description":"This classic textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The first half of the book gives an exposition of real analysis: basic set theory, general topology, measure theory, integration, an introduction to functional analysis in Banach and Hilbert spaces, convex sets and functions and measure on topological spaces. The second half introduces probability based on measure theory, including laws of large numbers, ergodic theorems, the central limit theorem, conditional expectations and martingale's convergence. A chapter on stochastic processes introduces Brownian motion and the Brownian bridge. The edition has been made even more self-contained than before; it now includes a foundation of the real number system and the Stone-Weierstrass theorem on uniform approximation in algebras of functions. Several other sections have been revised and improved, and the comprehensive historical notes have been further amplified. A number of new exercises have been added, together with hints for solution.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52141874544913,"sku":"NLS9780521809726","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52735456542993,"sku":"NIN9780521809726","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780521809726.jpg?v=1757578534"},{"product_id":"uniform-central-limit-theorems-book-r-m-dudley-9780521738415","title":"Uniform Central Limit Theorems","description":"This classic work on empirical processes has been considerably expanded and revised from the original edition. When samples become large, the probability laws of large numbers and central limit theorems are guaranteed to hold uniformly over wide domains. The author, an acknowledged expert, gives a thorough treatment of the subject, including the Fernique-Talagrand majorizing measure theorem for Gaussian processes, an extended treatment of Vapnik-Chervonenkis combinatorics, the Ossiander L2 bracketing central limit theorem, the Gin -Zinn bootstrap central limit theorem in probability, the Bronstein theorem on approximation of convex sets, and the Shor theorem on rates of convergence over lower layers. This new edition contains several proved theorems not included in the first edition, including the Bretagnolle-Massart theorem giving constants in the Komlos-Major-Tusnady rate of convergence for the classical empirical process, Massart's form of the Dvoretzky-Kiefer-Wolfowitz inequality with precise constant, Talagrand's generic chaining approach to boundedness of Gaussian processes, a characterization of uniform Glivenko-Cantelli classes of functions, Gin  and Zinn's characterization of uniform Donsker classes (i.e., classing Donsker uniformly over all probability measures P), and the Bousquet-Koltchinskii-Panchenko theorem that the convex hull of a uniform Donsker class is uniform Donsker. The book will be an essential reference for mathematicians working in infinite-dimensional central limit theorems, mathematical statisticians, and computer scientists working in computer learning theory. Problems are included at the end of each chapter so the book can also be used as an advanced text.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52343201202449,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52343201693969,"sku":"NLS9780521738415","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780521738415.jpg?v=1758173427"},{"product_id":"lectures-in-modern-analysis-and-applications-iii-book-r-m-dudley-9783540052845","title":"Lectures in Modern Analysis and Applications III","description":null,"brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52352822214929,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52352822739217,"sku":"NLS9783540052845","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540052845.jpg?v=1758182317"},{"product_id":"concrete-functional-calculus-book-r-m-dudley-9781441969491","title":"Concrete Functional Calculus","description":"Concrete Functional Calculus focuses primarily on differentiability of some nonlinear operators on functions or pairs of functions.  This  includes composition of two functions, and the product integral, taking a matrix- or operator-valued coefficient function into a solution of a system of linear differential equations with the given coefficients.  For nonlinear integral equations with respect to possibly discontinuous functions having unbounded variation, existence and uniqueness of solutions are proved under suitable assumptions.  Key features and topics:  * Extensive usage of p-variation of functions  * Applications to stochastic processes.  This work will serve as a thorough reference on its main topics for researchers and graduate students with a background in real analysis and, for Chapter 12, in probability.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52432506487057,"sku":"NLS9781441969491","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52749301350673,"sku":"NIN9781441969491","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781441969491.jpg?v=1759175174"},{"product_id":"concrete-functional-calculus-book-r-m-dudley-9781461427407","title":"Concrete Functional Calculus","description":"Concrete Functional Calculus focuses primarily on differentiability of some nonlinear operators on functions or pairs of functions.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52588661702929,"sku":"NLS9781461427407","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461427407.jpg?v=1761058515"},{"product_id":"uniform-central-limit-theorems-book-r-m-dudley-9780521498845","title":"Uniform Central Limit Theorems","description":"This classic work on empirical processes has been considerably expanded and revised from the original edition. When samples become large, the probability laws of large numbers and central limit theorems are guaranteed to hold uniformly over wide domains. The author, an acknowledged expert, gives a thorough treatment of the subject, including the Fernique-Talagrand majorizing measure theorem for Gaussian processes, an extended treatment of Vapnik-Chervonenkis combinatorics, the Ossiander L2 bracketing central limit theorem, the Gin -Zinn bootstrap central limit theorem in probability, the Bronstein theorem on approximation of convex sets, and the Shor theorem on rates of convergence over lower layers. This new edition contains several proved theorems not included in the first edition, including the Bretagnolle-Massart theorem giving constants in the Komlos-Major-Tusnady rate of convergence for the classical empirical process, Massart's form of the Dvoretzky-Kiefer-Wolfowitz inequality with precise constant, Talagrand's generic chaining approach to boundedness of Gaussian processes, a characterization of uniform Glivenko-Cantelli classes of functions, Gin  and Zinn's characterization of uniform Donsker classes (i.e., classing Donsker uniformly over all probability measures P), and the Bousquet-Koltchinskii-Panchenko theorem that the convex hull of a uniform Donsker class is uniform Donsker. The book will be an essential reference for mathematicians working in infinite-dimensional central limit theorems, mathematical statisticians, and computer scientists working in computer learning theory. Problems are included at the end of each chapter so the book can also be used as an advanced text.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52685470695697,"sku":"NLS9780521498845","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780521498845.jpg?v=1762325670"}],"url":"https:\/\/www.worldofbooks.com\/de-de\/collections\/autor-buecher-von-r-m-dudley.oembed","provider":"World of Books ","version":"1.0","type":"link"}