Integration - A Functional Approach (Paperback)

Klaus Bichteler

ISBN 10: 3034800541 / ISBN 13: 9783034800549

Published by Springer Basel, Basel, 2010

About this Item

Paperback. 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. This book covers Lebesgue integration and its generalizations from Daniell's point of view, modified by the use of seminorms. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9783034800549

Bibliographic Details

• Title: Integration - A Functional Approach (Paperback)
• Publisher: Springer Basel, Basel
• Publication Date: 2010
• Language: English
• ISBN 10: 3034800541
• ISBN 13: 9783034800549
• Binding: Paperback
• Edition: 1st Edition
• Condition: new

About this title

Synopsis

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.

About the Author

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