Integration - A Functional Approach (Birkhäuser Advanced Texts Basler Lehrbücher)

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9783764359362: Integration - A Functional Approach (Birkhäuser Advanced Texts Basler Lehrbücher)
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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.

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About the Author:

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

Review:

"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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9783034800549: Integration - A Functional Approach (Modern Birkhäuser Classics)

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Book Description Birkhauser. Hardcover. Condition: New. 208 pages. Dimensions: 9.4in. x 6.7in. x 0.6in.This book covers Lebesgue integration and its generalizations from Daniells 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 Lebesgues integral can be had as a rather straightforward, even simplistic, extension of Riemanns integral; and its aims, definitions, and procedures can be motivated at an elementary level. The notion of measurability, for example, is suggested by Littlewoods 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 item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Hardcover. Seller Inventory # 9783764359362

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Book Description Birkhauser Verlag AG, Switzerland, 1998. Hardback. Condition: New. 1998 ed.. Language: English . Brand New Book ***** Print on Demand *****.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. Seller Inventory # APC9783764359362

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