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Measure and Integration : Publications 1997-2011 / by Heinz König
版 | 1st ed. 2012. |
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出版者 | Basel : Springer Basel : Imprint: Birkhäuser |
出版年 | 2012 |
大きさ | XII, 512 p : online resource |
著者標目 | *König, Heinz author SpringerLink (Online service) |
件 名 | LCSH:Measure theory FREE:Measure and Integration |
一般注記 | Image measures and the so-called image measure catastrophe -- The product theory for inner premeasures -- Measure and Integration: Mutual generation of outer and inner premeasures -- Measure and Integration: Integral representations of isotone functionals -- Measure and Integration: Comparison of old and new procedures -- What are signed contents and measures?- Upper envelopes of inner premeasures -- On the inner Daniell-Stone and Riesz representation theorems -- Sublinear functionals and conical measures -- Measure and Integration: An attempt at unified systematization -- New facts around the Choquet integral -- The (sub/super)additivity assertion of Choquet -- Projective limits via inner premeasures and the trueWiener measure -- Stochastic processes in terms of inner premeasures -- New versions of the Radon-Nikodým theorem -- The Lebesgue decomposition theorem for arbitrary contents -- The new maximal measures for stochastic processes -- Stochastic processes on the basis of new measure theory -- New versions of the Daniell-Stone-Riesz representation theorem -- Measure and Integral: New foundations after one hundred years -- Fubini-Tonelli theorems on the basis of inner and outer premeasures -- Measure and Integration: Characterization of the new maximal contents and measures -- Notes on the projective limit theorem of Kolmogorov -- Measure and Integration: The basic extension theorems -- Measure Theory: Transplantation theorems for inner premeasures. This volume presents a collection of twenty-five of Heinz König’s recent and most influential works. Connecting to his book of 1997 “Measure and Integration”, the author has developed a consistent new version of measure theory over the past years. For the first time, his publications are collected here in one single volume. Key features include: - A first-time, original and entirely uniform treatment of abstract and topological measure theory - The introduction of the inner • and outer • premeasures and their extension to unique maximal measures - A simplification of the procedure formerly described in Chapter II of the author’s previous book - The creation of new “envelopes” for the initial set function (to replace the traditional Carathéodory outer measures), which lead to much simpler and more explicit treatment - The formation of products, a unified Daniell-Stone-Riesz representation theorem, and projective limits, which allows to obtain the Kolmogorov type projective limit theorem for even huge domains far beyond the countably determined ones - The incorporation of non-sequential and of inner regular versions, which leads to much more comprehensive results - Significant applications to stochastic processes. “Measure and Integration: Publications 1997–2011” will appeal to both researchers and advanced graduate students in the fields of measure and integration and probabilistic measure theory HTTP:URL=https://doi.org/10.1007/978-3-0348-0382-3 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783034803823 |
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電子リソース |
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EB00207784 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA312-312.5 DC23:515.42 |
書誌ID | 4000119617 |
ISBN | 9783034803823 |
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