| 書目名稱 | Integration - A Functional Approach | | 編輯 | Klaus Bichteler | | 視頻video | http://file.papertrans.cn/469/468773/468773.mp4 | | 概述 | 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 | | 叢書名稱 | Modern Birkh?user Classics | | 圖書封面 |  | | 描述 | .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 w | | 出版日期 | Book 1998 | | 關鍵詞 | Analysis; functional; Integral; Lebesgue integration; measure theory | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-0348-0055-6 | | isbn_softcover | 978-3-0348-0054-9 | | isbn_ebook | 978-3-0348-0055-6Series ISSN 2197-1803 Series E-ISSN 2197-1811 | | issn_series | 2197-1803 | | copyright | Birkh?user Verlag 1998 |
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