Klaus Bichteler

(Author)

Integration - A Functional Approach (1998)Paperback - 1998, 2 December 2010

Integration - A Functional Approach (1998)
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Part of Series
Modern Birkhäuser Classics
Print Length
197 pages
Language
English
Publisher
Birkhauser
Date Published
2 Dec 2010
ISBN-10
3034800541
ISBN-13
9783034800549

Description

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.

Product Details

Author:
Klaus Bichteler
Book Edition:
1998
Book Format:
Paperback
Country of Origin:
NL
Date Published:
2 December 2010
Dimensions:
23.39 x 15.6 x 1.09 cm
ISBN-10:
3034800541
ISBN-13:
9783034800549
Language:
English
Location:
Basel
Pages:
197
Publisher:
Weight:
290.3 gm

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