Integration : a functional approach
Author(s)
Bibliographic Information
Integration : a functional approach
（Birkhäuser advanced texts : Basler Lehrbücher / edited by Herbert Amann, Hanspeter Kraft）
Birkhäuser, c1998
- : Basel
- : Boston
Available at / 19 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: BaselBIC||2||398019225
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
: BaselDC21:515/B4712070445646
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Includes bibliographical references and indexes
Description and Table of Contents
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.
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
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