Integration - A Functional Approach by Klaus BichtelerIntegration - A Functional Approach by Klaus Bichteler

Integration - A Functional Approach

byKlaus Bichteler

Paperback | December 2, 2010

Pricing and Purchase Info

$72.62 online 
$75.95 list price
Earn 363 plum® points

Prices and offers may vary in store


In stock online

Ships free on orders over $25

Not available in stores


This book covers Lebesgue integration and its generalizations from Daniell's point of view, modified by the use of seminorms. Integrating functions rather than measuring sets is posited as the main purpose of measure theory.

From this point of view Lebesgue's integral can be had as a rather straightforward, even simplistic, extension of Riemann's integral; and its aims, definitions, and procedures can be motivated at an elementary level. The notion of measurability, for example, is suggested by Littlewood's observations rather than being conveyed authoritatively through definitions of (sigma)-algebras and good-cut-conditions, the latter of which are hard to justify and thus appear mysterious, even nettlesome, to the beginner. The approach taken provides the additional benefit of cutting the labor in half. The use of seminorms, ubiquitous in modern analysis, speeds things up even further.

The book is intended for the reader who has some experience with proofs, a beginning graduate student for example. It might even be useful to the advanced mathematician who is confronted with situations - such as stochastic integration - where the set-measuring approach to integration does not work.

Klaus Bichteler is a Professor of mathematics at the University of Texas.
Title:Integration - A Functional ApproachFormat:PaperbackDimensions:197 pagesPublished:December 2, 2010Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3034800541

ISBN - 13:9783034800549


Table of Contents

PrefaceChapter I ReviewChapter II Extension of the IntegralChapter III MeasurabilityChapter IV The Classical Banach SpacesChapter V Operations on MeasuresAppendix A Answers to Selected ProblemsReferencesIndex of NotationsIndex

Editorial Reviews

"One particularly valuable aspect of the book is that it gives a much richer discussion of Daniell's approach to integration than is usual. A generous supply of exercises is provided for each chapter. Answers to selected problems are given in an appendix."