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  • 实分析(英文版?第4版)[平装]
  • 共2个商家     35.77元~36.80
  • 作者:罗伊登(Royden.H.L.)(作者),菲茨帕特里克(Fitzpatrick.P.M.)(作者)
  • 出版社:机械工业出版社;第1版(2010年8月1日)
  • 出版时间:
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  • ISBN:9787111313052

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    《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。

    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.)

    目录

    Lebesgue Integration for Functions of a Single Real Variable
    Preliminaries on Sets, Mappings, and Relations
    Unions and Intersections of Sets
    Equivalence Relations, the Axiom of Choice, and Zorn's Lemma
    1 The Real Numbers: Sets. Sequences, and Functions
    The Field, Positivity, and Completeness Axioms
    The Natural and Rational Numbers
    Countable and Uncountable Sets
    Open Sets, Closed Sets, and Borel Sets of Real Numbers
    Sequences of Real Numbers
    Continuous Real-Valued Functions of a Real Variable
    2 Lebesgne Measure
    Introduction
    Lebesgue Outer Measure
    The o'-Algebra of Lebesgue Measurable Sets
    Outer and Inner Approximation of Lebesgue Measurable Sets
    Countable Additivity, Continuity, and the Borel-Cantelli Lemma
    Noumeasurable Sets
    The Cantor Set and the Cantor Lebesgue Function
    3 LebesgRe Measurable Functions
    Sums, Products, and Compositions
    Sequential Pointwise Limits and Simple Approximation
    Littlewood's Three Principles, Egoroff's Theorem, and Lusin's Theorem
    4 Lebesgue Integration
    The Riemann Integral
    The Lebesgue Integral of a Bounded Measurable Function over a Set of
    Finite Measure
    The Lebesgue Integral of a Measurable Nonnegative Function
    The General Lebesgue Integral
    Countable Additivity and Continuity of Integration
    Uniform Integrability: The Vifali Convergence Theorem
    viii Contents
    5 Lebusgue Integration: Fm'ther Topics
    Uniform Integrability and Tightness: A General Vitali Convergence Theorem
    Convergence in Measure
    Characterizations of Riemaun and Lebesgue Integrability
    6 Differentiation and Integration
    Continuity of Monotone Functions
    Differentiability of Monotone Functions: Lebesgue's Theorem
    Functions of Bounded Variation: Jordan's Theorem
    Absolutely Continuous Functions
    Integrating Derivatives: Differentiating Indefinite Integrals
    Convex Function
    7 The Lp Spaces: Completeness and Appro~umation
    Nor/ned Linear Spaces
    The Inequalities of Young, HOlder, and Minkowski
    Lv Is Complete: The Riesz-Fiseher Theorem
    Approximation and Separability
    8 The LP Spacesc Deailty and Weak Convergence
    The Riesz Representation for the Dual of
    Weak Sequential Convergence in Lv
    Weak Sequential Compactness
    The Minimization of Convex Functionals
    II Abstract Spaces: Metric, Topological, Banach, and Hiibert Spaces
    9. Metric Spaces: General Properties
    Examples of Metric Spaces
    Open Sets, Closed Sets, and Convergent Sequences
    Continuous Mappings Between Metric Spaces
    Complete Metric Spaces
    Compact Metric Spaces
    Separable Metric Spaces
    10 Metric Spaces: Three Fundamental Thanreess
    The Arzelb.-Ascoli Theorem
    The Baire Category Theorem
    The Banaeh Contraction Principle
    H Topological Spaces: General Properties
    Open Sets, Closed Sets, Bases, and Subbases
    The Separation Properties
    Countability and Separability
    Continuous Mappings Between Topological Spaces

    Compact Topological Spaces
    Connected Topological Spaces
    12 Topological Spaces: Three Fundamental Theorems
    Urysohn's Lemma and the Tietze Extension Theorem
    The Tychonoff Product Theorem
    The Stone-Weierstrass Theorem
    13 Continuous Linear Operators Between Bausch Spaces
    Normed Linear Spaces
    Linear Operators
    Compactness Lost: Infinite Dimensional Normod Linear Spaces
    The Open Mapping and Closed Graph Theorems
    The Uniform Boundedness Principle
    14 Duality for Normed Iinear Spaces
    Linear Ftmctionals, Bounded Linear Functionals, and Weak Topologies
    The Hahn-Banach Theorem
    Reflexive Banach Spaces and Weak Sequential Convergence
    Locally Convex Topological Vector Spaces
    The Separation of Convex Sets and Mazur's Theorem
    The Krein-Miiman Theorem
    15 Compactness Regained: The Weak Topology
    Alaoglu's Extension of Helley's Theorem
    Reflexivity and Weak Compactness: Kakutani's Theorem
    Compactness and Weak Sequential Compactness: The Eberlein-mulian
    Theorem
    Memzability of Weak Topologies
    16 Continuous Linear Operators on Hilbert Spaces
    The Inner Product and Orthogonality
    The Dual Space and Weak Sequential Convergence
    Bessers Inequality and Orthonormal Bases
    bAdjoints and Symmetry for Linear Operators
    Compact Operators
    The Hilbert-Schmidt Theorem
    The Riesz-Schauder Theorem: Characterization of Fredholm Operators
    Measure and Integration: General Theory
    17 General Measure Spaces: Their Propertles and Construction
    Measures and Measurable Sets
    Signed Measures: The Hahn and Jordan Decompositions
    The Caratheodory Measure Induced by an Outer Measure
    18 Integration Oeneral Measure Spaces
    19 Gengral L Spaces:Completeness,Duality and Weak Convergence
    20 The Construciton of Particular Measures
    21 Measure and Topbogy
    22 Invariant Measures
    Bibiiography
    index

    序言

    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.

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