Integration - A Functional Approach (Hardcover)

Klaus Bichteler

ISBN 10: 3764359366 / ISBN 13: 9783764359362

Editore: Birkhauser Verlag AG, Basel, 1998

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Hardcover. This text 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 in the book. It is intended for the reader who has some experience with proofs, and for those confronted with situations such as stochastic integration - where the set-measuring approach to integration does not work. The book covers Lebesque integration and its generalisations from Daniell's point of view, modified by the use of seminorms. It gives motivations for the constructions, procedures, and definitions employed in measure theory, rather than confronting the reader with formal definitions. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

Codice articolo 9783764359362

Dati bibliografici

• Titolo: Integration - A Functional Approach (Hardcover)
• Editore: Birkhauser Verlag AG, Basel
• Data di pubblicazione: 1998
• Lingua: Inglese
• ISBN 10: 3764359366
• ISBN 13: 9783764359362
• Rilegatura: Hardcover
• Condizione: new

Descrizione articolo

Riassunto

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.

Informazioni sull?autore

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