实分析(Real Analysis)英文版[DJVU]

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资源信息： 中文名: 实分析 原名: Real Analysis 作者: DiBenedetto Carothers Bichteler 图书分类: 科技 资源格式: DJVU 版本: 英文版 出版社: Birkhauser 书号: 0817642315 发行时间: 2002年 地区: 德国 语言: 英文 概述:

djvu 电子书阅读器： http://windjview.sourceforge.net/ 内容简介： 本书是一本内容十分翔实的实分析教材。它包含集论，点集拓扑。测度与积分，Lebesgue函数空间，Banach空间与Hilbert空间，连续函数空间，广义函数与弱导数，Sobolev空间与Sobolev嵌入定理等；同时还包含 Lebesgue微分定理，Stone-Weierstrass逼近定理，Ascoli—Arzela定理， Calderon—Zygmund分解定理，Fefferman—Stein定理。Marcinkiewlcz插定理等实分析中有用的内容。 　　本书内容由浅入深。读者具有扎实的数学分析知识基础便可学习本书，学完本书的读者将具备学习分析所需要的实变与泛函(不包括算子理论)的准备知识和训练。 内容截图：

目录: Preface Acknowledgments Preliminaries 1 Countable sets 2 The Cantor set 3 Cardinality 3.1 Some examples 4 Cardinality of some infinite Cartesian products 5 Orderings, the maximal principle, and the axiom of choice 6 Well-ordering 6.1 The first uncountable Problems and Complements Ⅰ Topologies and Metric Spaces 1 Topological spaces 1.1 Hausdorff and normal spaces 2 Urysohn's lemma 3 The Tietze extension theorem 4 Bases, axioms of countability, and product topologies 4.1 Product topologies 5 Compact topological spaces 5.1 Sequentially compact topological spaces 6 Compact subsets of RN 7 Continuous functions on countably compact spaces 8 Products of compact spaces 9 Vector spaces 9.1 Convex sets 9.2 Linear maps and isomorphisms 10 Topological vector spaces 10.1 Boundedness and continuity 11 Linear functionals 12 Finite-dimensional topological vector spaces 12.1 Locally compact spaces 13 Metric spaces 13.1 Separation and axioms of countability 13.2 Equivalent metrics 13.3 Pseudometrics 14 Metric vector spaces 14.1 Maps between metric spaces 15 Spaces of continuous functions 15.1 Spaces of continuously differentiable functions 16 On the structure of a complete metric space 17 Compact and totally bounded metric spaces 17.1 Precompact subsets of X Problems and Complements Ⅱ Measuring Sets 1 Partitioning open subsets of RN 2 Limits of sets, characteristic functions, and or-algebras 3 Measures 3.1 Finite,a-finite, and complete measures 3.2 Some examples 4 Outer measures and sequential coverings 4.1 The Lebesgue outer measure in RN 4.2 The Lebesgue-Stieltjes outer measure 5 The Hausdorff outer measure in RN 6 Constructing measures from outer measures 7 The Lebesgue--Stieltjes measure on R 7.1 Borel measures 8 The Hausdorff measure on RN 9 Extending measures from semialgebras to a-algebras 9.1 On the Lebesgue-Stieltjes and Hausdorff measures 10 Necessary and sufficient conditions for measurability 11 More on extensions from semialgebras to a-algebras 12 The Lebesgue measure of sets in RN 12.1 A necessary and sufficient condition of naeasurability 13 A nonmeasurable set …… Ⅲ The Lebesgue Integral Ⅳ Topics on Measurable Functions of Real Variables Ⅴ The Lp(E)Spaces Ⅵ Banach Spaces Ⅶ Spaces of Continuous Functions,Distributions,and Weak Ⅷ Topics on Integrable Functions of Real Variables Ⅸ Embeddings of W1,p(E)into Lq(E) References Index