Measure Theory and Integration by Michael E Taylor

Measure Theory and Integration by Michael E Taylor

This self-contained treatment of measure and integration begins with a brief review of the Riemann integral and proceeds to a construction of Lebesgue measure on the real line. From there the reader is led to the general notion of measure, to the construction of the Lebesgue integral on a measure space, and to the major limit theorems, such as the Monotone and Dominated Convergence Theorems. The treatment proceeds to $L^p$ spaces, normed linear spaces that are shown to be complete (i.e., Banach spaces) due to the limit theorems. Particular attention is paid to $L^2$ spaces as Hilbert spaces, with a useful geometrical structure. Having gotten quickly to the heart of the matter, the text proceeds to broaden its scope. There are further constructions of measures, including Lebesgue measure on $n$-dimensional Euclidean space. There are also discussions of surface measure, and more generally of Riemannian manifolds and the measures they inherit, and an appendix on the integration of differential forms. Further geometric aspects are explored in a chapter on Hausdorff measure. The text also treats probabilistic concepts, in chapters on ergodic theory, probability spaces and random variables, Wiener measure and Brownian motion, and martingales. This text will prepare graduate students for more advanced studies in functional analysis, harmonic analysis, stochastic analysis, and geometric measure theory.

Taylor's treatment throughout is elegant and very efficient.. I found reading the text very enjoyable."" —MAA Reviews

""The book is very understandable, requiring only a basic knowledge of analysis. It can be warmly recommended to a broad spectrum of readers, to graduate students as well as young researchers."" —EMS Newsletter

""This monograph provides a quite comprehensive presentation of measure and integration theory and of some of their applications."" —Mathematical Reviews

Michael E. Taylor, University of North Carolina, Chapel Hill, NC.

SKU	Unavailable
ISBN 13	9781470484767
ISBN 10	1470484765
Title	Measure Theory and Integration
Author	Michael E Taylor
Series	Graduate Studies In Mathematics
Condition	Unavailable
Binding Type	Paperback
Publisher	American Mathematical Society
Year published	2006-01-30
Number of pages	319
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.