Authors:
- Complete and rapid introduction to Lebesgue integration and its generalization
- Unusually detailed discussion of Percy Daniell’s functional analytic approach to integration
- Complemented by interesting historical notes and motivations
- Provides numerous exercises and solutions / hints for selected problems
- Includes supplementary material: sn.pub/extras
Part of the book series: Modern Birkhäuser Classics (MBC)
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Table of contents (6 chapters)
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Front Matter
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Back Matter
About this book
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.
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."
--ZAA
Authors and Affiliations
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, Department of Mathematics, The University of Texas, Austin, USA
Klaus Bichteler
About the author
Bibliographic Information
Book Title: Integration - A Functional Approach
Authors: Klaus Bichteler
Series Title: Modern Birkhäuser Classics
DOI: https://doi.org/10.1007/978-3-0348-0055-6
Publisher: Birkhäuser Basel
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eBook Packages: Springer Book Archive
Copyright Information: Birkh�user Verlag 1998
Hardcover ISBN: 978-3-7643-5936-2Published: 19 May 1998
Softcover ISBN: 978-3-0348-0054-9Published: 02 December 2010
eBook ISBN: 978-3-0348-0055-6Published: 23 November 2010
Series ISSN: 2197-1803
Series E-ISSN: 2197-1811
Edition Number: 1
Number of Pages: VIII, 197
Topics: Functional Analysis