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Birkhäuser Advanced Texts Basler Lehrbücher

Integration - A Functional Approach

Authors: Bichteler, Klaus

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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

This book provides a complete and rapid introduction to Lebesgue integration and its generalizations from Daniell’s point of view, (…) The development is clear and it contains interesting historical notes and motivations, abundant exercises and many supplements. The connection with the historical development of integration theory is also pointed out.
- Zentralblatt MATH

The material is well motivated and the writing is pleasantly informal. (…) There are numerous exercises, many destined to be used later in the text, and 15 pages of solutions/hints.
- Mathematical Reviews

About the authors

Klaus Bichteler is a Professor of mathematics at the University of Texas.

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


Table of contents (6 chapters)

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-0348-0055-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-3-7643-5936-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.99
price for USA
  • ISBN 978-3-0348-0054-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Integration - A Functional Approach
Authors
Series Title
Birkhäuser Advanced Texts Basler Lehrbücher
Copyright
1998
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Verlag
eBook ISBN
978-3-0348-0055-6
DOI
10.1007/978-3-0348-0055-6
Hardcover ISBN
978-3-7643-5936-2
Softcover ISBN
978-3-0348-0054-9
Series ISSN
1019-6242
Edition Number
1
Number of Pages
VIII, 197
Topics