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Lectures on Functional Analysis and the Lebesgue Integral / by Vilmos Komornik
(Universitext. ISSN:21916675)
版 | 1st ed. 2016. |
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出版者 | (London : Springer London : Imprint: Springer) |
出版年 | 2016 |
大きさ | XX, 403 p. 46 illus : online resource |
著者標目 | *Komornik, Vilmos author SpringerLink (Online service) |
件 名 | LCSH:Functional analysis LCSH:Measure theory LCSH:Approximation theory FREE:Functional Analysis FREE:Measure and Integration FREE:Approximations and Expansions |
一般注記 | Some papers of general interest -- Topological prerequisites -- Part 1 Functional analysis -- Hilbert spaces -- Banach spaces -- Locally convex spaces -- Part 2 The Lebesgue integral -- Monotone functions.- The Lebesgue integral in R -- Generalized Newton-Leibniz formula -- Integrals on measure spaces -- Part 3 Function spaces.- Spaces of continuous functions -- Spaces of integrable functions -- Almost everywhere convergence -- Hints and solutions to some exercises.- Bibliography -- Teaching remarks -- Subject index -- Name index This textbook, based on three series of lectures held by the author at the University of Strasbourg, presents functional analysis in a non-traditional way by generalizing elementary theorems of plane geometry to spaces of arbitrary dimension. This approach leads naturally to the basic notions and theorems. Most results are illustrated by the small ℓp spaces. The Lebesgue integral, meanwhile, is treated via the direct approach of Frigyes Riesz, whose constructive definition of measurable functions leads to optimal, clear-cut versions of the classical theorems of Fubini-Tonelli and Radon-Nikodým. Lectures on Functional Analysis and the Lebesgue Integral presents the most important topics for students, with short, elegant proofs. The exposition style follows the Hungarian mathematical tradition of Paul Erdős and others. The order of the first two parts, functional analysis and the Lebesgue integral, may be reversed. In the third and final part they are combined to study various spaces of continuous and integrable functions. Several beautiful, but almost forgotten, classical theorems are also included. Both undergraduate and graduate students in pure and applied mathematics, physics and engineering will find this textbook useful. Only basic topological notions and results are used and various simple but pertinent examples and exercises illustrate the usefulness and optimality of most theorems. Many of these examples are new or difficult to localize in the literature, and the original sources of most notions and results are indicated to help the reader understand the genesis and development of the field HTTP:URL=https://doi.org/10.1007/978-1-4471-6811-9 |
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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 | 9781447168119 |
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EB00201684 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA319-329.9 DC23:515.7 |
書誌ID | 4000117868 |
ISBN | 9781447168119 |
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※2017年9月4日以降