his 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 thispoint 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 readerwho has some experience with proofs, a beginning graduate student for example. It might even be useful to the advanced mathematician who is confronted withsituations - such as stochastic integration - where the set-measuring approach to integration does not work. " Complete and rapid introduction to Lebesgue integration and its generalization Unusually detailed discussion of Percy Daniell’s functional analytic approach to integration Complemented by interesting historical notes and motivations Provides numerous exercises and solutions / hints for selected problems INDICE: 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.
- ISBN: 978-3-0348-0054-9
- Editorial: Birkhaüser
- Encuadernacion: Rústica
- Páginas: 193
- Fecha Publicación: 01/12/2010
- Nº Volúmenes: 1
- Idioma: Inglés