Measure and Integration Theory

Heinz Bauer

Published by De Gruyter 2001

Measure and Integration Theory

Heinz Bauer
Translated by: Robert B. Burckel

Volume 26 in the series De Gruyter Studies in Mathematics

https://doi.org/10.1515/9783110866209

Overview
Contents

About this book

This book gives a straightforward introduction to the field as it is nowadays required in many branches of analysis and especially in probability theory. The first three chapters (Measure Theory, Integration Theory, Product Measures) basically follow the clear and approved exposition given in the author's earlier book on "Probability Theory and Measure Theory". Special emphasis is laid on a complete discussion of the transformation of measures and integration with respect to the product measure, convergence theorems, parameter depending integrals, as well as the Radon-Nikodym theorem.

The final chapter, essentially new and written in a clear and concise style, deals with the theory of Radon measures on Polish or locally compact spaces. With the main results being Luzin's theorem, the Riesz representation theorem, the Portmanteau theorem, and a characterization of locally compact spaces which are Polish, this chapter is a true invitation to study topological measure theory.

The text addresses graduate students, who wish to learn the fundamentals in measure and integration theory as needed in modern analysis and probability theory. It will also be an important source for anyone teaching such a course.

Author / Editor information

Professor Heinz Bauer (1928--2002) was Professor at the Mathematical Institute of the Friedrich-Alexander-University Erlangen-Nürnberg, Erlangen, Germany.

Reviews

"It is a pleasure to see Heinz Bauer's famous monograph Maß- und Intergrationstheorie [...] published in English. [...] The translation by Robert B. Burckel is careful and close to the German original. He has replaced references to German textbooks by references to English textbooks, and he has also added several interesting exercises, comments, and references. the typographical appearance of the book is excellent." Zentralblatt für Mathematik

"Like the German original, the present textbook is a very readable and concise introduction to measure theory and integration.[...] In any case, it definitely is a valuable resource for both students and teachers." Internationale Mathematische Nachrichten

"I am certain that this very attractive treatment of the theory of measure and integration will receive the same enthusiastic reception as the original German edition." Mathematical Reviews

Topics

Frontmatter Requires Authentication Unlicensed Licensed Download PDF	I
Chapter I Measure Theory Requires Authentication Unlicensed Licensed Download PDF	1
Chapter II Integration Theory Requires Authentication Unlicensed Licensed Download PDF	49
Chapter III Product Measures Requires Authentication Unlicensed Licensed Download PDF	132
Chapter IV Measures on Topological Spaces Requires Authentication Unlicensed Licensed Download PDF	152
Bibliography Requires Authentication Unlicensed Licensed Download PDF	217
Symbol Index Requires Authentication Unlicensed Licensed Download PDF	221
Name Index Requires Authentication Unlicensed Licensed Download PDF	223
Subject Index Requires Authentication Unlicensed Licensed Download PDF	225
Backmatter Requires Authentication Unlicensed Licensed Download PDF	231

(Deutsch)

Language: English
Publisher: De Gruyter
Pages
- Front matter: 16
- Main content: 230
Keywords: Mass (Math.); Integral

eBook

Published: April 20, 2011
ISBN: 9783110866209

Hardcover

Published: June 21, 2001
ISBN: 9783110167191