Integration - A Functional Approach
(Sprache: Englisch)
This volume covers Lebesgue integration and its generalizations from Daniell's point of view, modified by the use of seminorms. The integration of functions, as opposed to the measuring of sets, is posited as the main purpose of measure theory.
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This volume covers Lebesgue integration and its generalizations from Daniell's point of view, modified by the use of seminorms. The integration of functions, as opposed to the measuring of sets, is posited as the main purpose of measure theory.
Klappentext zu „Integration - A Functional Approach “
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.
Inhaltsverzeichnis zu „Integration - A Functional Approach “
Preface Chapter I Review
Chapter II Extension of the Integral
Chapter III Measurability
Chapter IV The Classical Banach Spaces
Chapter V Operations on Measures
Appendix A Answers to Selected Problems
References
Index of Notations Index
Autoren-Porträt von Klaus Bichteler
Klaus Bichteler is a Professor of mathematics at the University of Texas.
Bibliographische Angaben
- Autor: Klaus Bichteler
- 1998, 212 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer Basel
- ISBN-10: 3764359366
- ISBN-13: 9783764359362
- Erscheinungsdatum: 19.05.1998
Sprache:
Englisch
Rezension zu „Integration - A Functional Approach “
"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
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