測度と積分論<br>Measure and Integration Theory (De Gruyter Studies in Mathematics 26) （2001. XVI, 230 S. 230 mm）

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測度と積分論
Measure and Integration Theory (De Gruyter Studies in Mathematics 26) （2001. XVI, 230 S. 230 mm）

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  • 製本 Hardcover:ハードカバー版／ページ数 236 p.
  • 言語 ENG
  • 商品コード 9783110167191

基本説明

Translated from the German by Robert B. Burckel. Gives a straightforward introduction to the field as it is nowadays required in many branches of analysis and expecially in probability theory.

Description


(Short description)

(Text)

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.

(Table of content)

Measure Theory Integration Theory Product Measures Measures on Topological Spaces Bibliography Index

(Review)

"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