实分析

出版时间：2010-8  出版社：机械工业出版社  作者：罗伊登(Royden.H.L.),菲茨帕特里克(Fitzpatrick.P.M.)  页数：505  
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前言

The first three editions of H．］．Royden’S Real Analysis have contributed to the education of generation so fm a them atical analysis students．This four the dition of Real Analysispreservesthe goal and general structure of its venerable predecessors——to present the measure theory．integration theory．and functional analysis that a modem analyst needs to know．The book is divided the three parts：Part I treats Lebesgue measure and Lebesgueintegration for functions of a single real variable；Part II treats abstract spaces topological spaces，metric spaces，Banach spaces，and Hilbert spaces；Part III treats integration over general measure spaces．together with the enrichments possessed by the general theory in the presence of topological，algebraic，or dynamical structure．The material in Parts II and III does not formally depend on Part I．However．a careful treatment of Part I provides the student with the opportunity to encounter new concepts in afamiliar setting，which provides a foundation and motivation for the more abstract conceptsdeveloped in the second and third parts．Moreover．the Banach spaces created in Part I．theLp spaces，are one of the most important dasses of Banach spaces．The principal reason forestablishing the completeness of the Lp spaces and the characterization of their dual spacesiS to be able to apply the standard tools of functional analysis in the study of functionals andoperators on these spaces．The creation of these tools is the goal of Part II．

内容概要

　 《实分析（英文版·第4版）》是实分析课程的优秀教材，被国外众多著名大学（如斯坦福大学、哈佛大学等）采用。全书分为三部分：第一部分为实变函数论.介绍一元实变函数的勒贝格测度和勒贝格积分:第二部分为抽象空间。介绍拓扑空间、度量空间、巴拿赫空间和希尔伯特空间；第三部分为一般测度与积分理论。介绍一般度量空间上的积分.以及拓扑、代数和动态结构的一般理论。书中不仅包含数学定理和定义，而且还提出了富有启发性的问题，以便读者更深入地理解书中内容。

作者简介

作者：（美国）罗伊登（Royden.H.L.） （美国）菲茨帕特里克（Fitzpatrick.P.M.）

书籍目录

Lebesgue Integration for Functions of a Single Real VariablePreliminaries on Sets, Mappings, and RelationsUnions and Intersections of SetsEquivalence Relations, the Axiom of Choice, and Zorn's Lemma 1 The Real Numbers: Sets. Sequences, and FunctionsThe Field, Positivity, and Completeness AxiomsThe Natural and Rational NumbersCountable and Uncountable SetsOpen Sets, Closed Sets, and Borel Sets of Real Numbers Sequences of Real NumbersContinuous Real-Valued Functions of a Real Variable2 Lebesgne MeasureIntroductionLebesgue Outer MeasureThe o'-Algebra of Lebesgue Measurable SetsOuter and Inner Approximation of Lebesgue Measurable Sets  Countable Additivity, Continuity, and the Borel-Cantelli LemmaNoumeasurable SetsThe Cantor Set and the Cantor Lebesgue Function3 LebesgRe Measurable FunctionsSums, Products, and CompositionsSequential Pointwise Limits and Simple ApproximationLittlewood's Three Principles, Egoroff's Theorem, and Lusin's Theorem4 Lebesgue IntegrationThe Riemann IntegralThe Lebesgue Integral of a Bounded Measurable Function over a Set ofFinite MeasureThe Lebesgue Integral of a Measurable Nonnegative FunctionThe General Lebesgue IntegralCountable Additivity and Continuity of IntegrationUniform Integrability: The Vifali Convergence Theoremviii Contents5 Lebusgue Integration: Fm'ther TopicsUniform Integrability and Tightness: A General Vitali Convergence TheoremConvergence in MeasureCharacterizations of Riemaun and Lebesgue Integrability6 Differentiation and IntegrationContinuity of Monotone FunctionsDifferentiability of Monotone Functions: Lebesgue's TheoremFunctions of Bounded Variation: Jordan's TheoremAbsolutely Continuous FunctionsIntegrating Derivatives: Differentiating Indefinite IntegralsConvex Function7 The Lp Spaces: Completeness and Appro~umationNor/ned Linear SpacesThe Inequalities of Young, HOlder, and Minkowski Lv Is Complete: The Riesz-Fiseher TheoremApproximation and Separability8 The LP Spacesc Deailty and Weak ConvergenceThe Riesz Representation for the Dual ofWeak Sequential Convergence in Lv  Weak Sequential CompactnessThe Minimization of Convex FunctionalsII  Abstract Spaces: Metric, Topological, Banach, and Hiibert Spaces9. Metric Spaces: General PropertiesExamples of Metric SpacesOpen Sets, Closed Sets, and Convergent SequencesContinuous Mappings Between Metric Spaces Complete Metric SpacesCompact Metric SpacesSeparable Metric Spaces10 Metric Spaces: Three Fundamental ThanreessThe Arzelb.-Ascoli TheoremThe Baire Category TheoremThe Banaeh Contraction PrincipleH Topological Spaces: General PropertiesOpen Sets, Closed Sets, Bases, and SubbasesThe Separation PropertiesCountability and SeparabilityContinuous Mappings Between Topological SpacesCompact Topological SpacesConnected Topological Spaces12 Topological Spaces: Three Fundamental TheoremsUrysohn's Lemma and the Tietze Extension Theorem The Tychonoff Product TheoremThe Stone-Weierstrass Theorem13 Continuous Linear Operators Between Bausch SpacesNormed Linear SpacesLinear OperatorsCompactness Lost: Infinite Dimensional Normod Linear SpacesThe Open Mapping and Closed Graph TheoremsThe Uniform Boundedness Principle14 Duality for Normed Iinear SpacesLinear Ftmctionals, Bounded Linear Functionals, and Weak TopologiesThe Hahn-Banach TheoremReflexive Banach Spaces and Weak Sequential ConvergenceLocally Convex Topological Vector SpacesThe Separation of Convex Sets and Mazur's TheoremThe Krein-Miiman Theorem15 Compactness Regained: The Weak TopologyAlaoglu's Extension of Helley's TheoremReflexivity and Weak Compactness: Kakutani's TheoremCompactness and Weak Sequential Compactness: The Eberlein-mulianTheoremMemzability of Weak Topologies 16 Continuous Linear Operators on Hilbert SpacesThe Inner Product and OrthogonalityThe Dual Space and Weak Sequential ConvergenceBessers Inequality and Orthonormal BasesbAdjoints and Symmetry for Linear OperatorsCompact OperatorsThe Hilbert-Schmidt TheoremThe Riesz-Schauder Theorem: Characterization of Fredholm Operators Measure and Integration: General Theory17 General Measure Spaces: Their Propertles and ConstructionMeasures and Measurable SetsSigned Measures: The Hahn and Jordan Decompositions  The Caratheodory Measure Induced by an Outer Measure18 Integration Oeneral Measure Spaces19 Gengral L Spaces:Completeness,Duality and Weak Convergence20 The Construciton of Particular Measures21 Measure and Topbogy22 Invariant MeasuresBibiiographyindex

章节摘录

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编辑推荐

《实分析(英文版·第4版)》 :新增了50％的习题。扩充了基本结果。包括给出叶果洛夫定理和乌霄松引理的证明。介绍了博雷尔一坎特利引理、切比霄夫不等式、快速柯西序列及测度和积分所共有的连续性质.以及若干其他概念。

用户评论 (总计13条)

•   看到之前一些朋友的评论，本来不打算买了，但是还是冲着是经典书买了下来。印刷感觉很好，是小了点，但是绝对很清楚，斜体字，黑体都很清楚，我看过原版第三版，用的纸很厚，因此整本书很厚；但是这本机工出的第四版的，拿着很顺手，携带起来会很方便。内容就不用多说了，作者从一维的勒比格积分讲起，再拓展到抽象空间，题目量多质好，而且第三版的网上有答案，据说第四版的增添了50%的题目，还没开始看。应该不会令人失望。总体感觉机工的书在印刷质量上比世图的好，我辈有幸，能花这些钱就看到原版书。我热忱推荐给各位读者朋友。
•   刚拿到书，发货速度非常慢，而且书还损坏了
•   书是非常好的，但是运过来的时候有点破损，后来波波折折还了一本 不过还是感谢店家了！ 这书非常适合我
•   书很好，字很清楚，服务很好
•   相当不错的一本书！很喜欢
•   速度很快~服务很好~就是字太小了~~如果字大些就好了~~
•   字太小了，出版社能不能以后改改，严重影响阅读！ 当然，书的内容还是一流的
•   感觉字有点小，纸张有点薄。。
•   比华章artin的algebra要小一号，字就比较小了，看起来吃力。
•   书很好，提前买回来，慢慢研究。有时可做了。
•   书写的不错，内容翔实，阐述清晰。就是这个印刷，坑爹啊。印成了小24开，字的size像paper上的一样小。机械工业出版社太不给力了
•   书是经典的 但有其它更好的选择
•   非常精彩的一本书，吃透可成一家。