| 书目名称 | Measure and Integration | | 副标题 | An Advanced Course i | | 编辑 | Heinz König | | 视频video | | | 概述 | Includes supplementary material: | | 图书封面 |  | | 描述 | .This book sets out to restructure certain fundamentals in measure and integration theory, and thus to fee the theory from some notorious drawbacks. It centers around the ubiquitous task of producing appropriate contents and measures from more primitive data, in order to extend elementary contents and to represent elementary integrals. This task has not been met with adequate unified means so far. The traditional main tools, the Carathéodory and Daniell-Stone theorems, are too restrictive and had to be supplemented by other ad-hoc procedures. Around 1970 a new approach emerged, based on the notion of regularity, which in traditional measure theory is linked to topology. The present book develops the new approach into a systematic theory. The theory unifies the entire context and is much more powerful than the former means. It has striking implications all over measure theory and beyond. Thus it extends the Riesz representation theorem in terms of Randon measures from locally compact to arbitrary Hausdorff topological spaces. It furthers the methodical unification with non-additive set functions, as shown in natural extensions of the Choquet capacitability theorem. The presentation | | 出版日期 | Book 1997 | | 关键词 | capacity; construction of measures; integral; integral representation; integration; measure; measure theor | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-540-89502-2 | | isbn_softcover | 978-3-642-08277-1 | | isbn_ebook | 978-3-540-89502-2 | | copyright | Springer-Verlag Berlin Heidelberg 1997 |
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发表于 2025-3-21 16:08:49
