实分析(英文版·第4版)

实分析(英文版·第4版)
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作者: [美] (Royden.H.L.) (Fitzpatrick.P.M.)
出版社: 机械工业出版社
2010-08
版次: 4
ISBN: 9787111313052
定价: 49.00
装帧: 平装
开本: 16开
纸张: 胶版纸
页数: 505页
正文语种: 英语
分类: 自然科学
  • 《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。 LebesgueIntegrationforFunctionsofaSingleRealVariable
    PreliminariesonSets,Mappings,andRelations
    UnionsandIntersectionsofSets
    EquivalenceRelations,theAxiomofChoice,andZorn'sLemma
    1TheRealNumbers:Sets.Sequences,andFunctions
    TheField,Positivity,andCompletenessAxioms
    TheNaturalandRationalNumbers
    CountableandUncountableSets
    OpenSets,ClosedSets,andBorelSetsofRealNumbers
    SequencesofRealNumbers
    ContinuousReal-ValuedFunctionsofaRealVariable
    2LebesgneMeasure
    Introduction
    LebesgueOuterMeasure
    Theo'-AlgebraofLebesgueMeasurableSets
    OuterandInnerApproximationofLebesgueMeasurableSets
    CountableAdditivity,Continuity,andtheBorel-CantelliLemma
    NoumeasurableSets
    TheCantorSetandtheCantorLebesgueFunction
    3LebesgReMeasurableFunctions
    Sums,Products,andCompositions
    SequentialPointwiseLimitsandSimpleApproximation
    Littlewood'sThreePrinciples,Egoroff'sTheorem,andLusin'sTheorem
    4LebesgueIntegration
    TheRiemannIntegral
    TheLebesgueIntegralofaBoundedMeasurableFunctionoveraSetof
    FiniteMeasure
    TheLebesgueIntegralofaMeasurableNonnegativeFunction
    TheGeneralLebesgueIntegral
    CountableAdditivityandContinuityofIntegration
    UniformIntegrability:TheVifaliConvergenceTheorem
    viiiContents
    5LebusgueIntegration:Fm'therTopics
    UniformIntegrabilityandTightness:AGeneralVitaliConvergenceTheorem
    ConvergenceinMeasure
    CharacterizationsofRiemaunandLebesgueIntegrability
    6DifferentiationandIntegration
    ContinuityofMonotoneFunctions
    DifferentiabilityofMonotoneFunctions:Lebesgue'sTheorem
    FunctionsofBoundedVariation:Jordan'sTheorem
    AbsolutelyContinuousFunctions
    IntegratingDerivatives:DifferentiatingIndefiniteIntegrals
    ConvexFunction
    7TheLpSpaces:CompletenessandAppro~umation
    Nor/nedLinearSpaces
    TheInequalitiesofYoung,HOlder,andMinkowski
    LvIsComplete:TheRiesz-FiseherTheorem
    ApproximationandSeparability
    8TheLPSpacescDeailtyandWeakConvergence
    TheRieszRepresentationfortheDualof
    WeakSequentialConvergenceinLv
    WeakSequentialCompactness
    TheMinimizationofConvexFunctionals
    IIAbstractSpaces:Metric,Topological,Banach,andHiibertSpaces
    9.MetricSpaces:GeneralProperties
    ExamplesofMetricSpaces
    OpenSets,ClosedSets,andConvergentSequences
    ContinuousMappingsBetweenMetricSpaces
    CompleteMetricSpaces
    CompactMetricSpaces
    SeparableMetricSpaces
    10MetricSpaces:ThreeFundamentalThanreess
    TheArzelb.-AscoliTheorem
    TheBaireCategoryTheorem
    TheBanaehContractionPrinciple
    HTopologicalSpaces:GeneralProperties
    OpenSets,ClosedSets,Bases,andSubbases
    TheSeparationProperties
    CountabilityandSeparability
    ContinuousMappingsBetweenTopologicalSpaces

    CompactTopologicalSpaces
    ConnectedTopologicalSpaces
    12TopologicalSpaces:ThreeFundamentalTheorems
    Urysohn'sLemmaandtheTietzeExtensionTheorem
    TheTychonoffProductTheorem
    TheStone-WeierstrassTheorem
    13ContinuousLinearOperatorsBetweenBauschSpaces
    NormedLinearSpaces
    LinearOperators
    CompactnessLost:InfiniteDimensionalNormodLinearSpaces
    TheOpenMappingandClosedGraphTheorems
    TheUniformBoundednessPrinciple
    14DualityforNormedIinearSpaces
    LinearFtmctionals,BoundedLinearFunctionals,andWeakTopologies
    TheHahn-BanachTheorem
    ReflexiveBanachSpacesandWeakSequentialConvergence
    LocallyConvexTopologicalVectorSpaces
    TheSeparationofConvexSetsandMazur'sTheorem
    TheKrein-MiimanTheorem
    15CompactnessRegained:TheWeakTopology
    Alaoglu'sExtensionofHelley'sTheorem
    ReflexivityandWeakCompactness:Kakutani'sTheorem
    CompactnessandWeakSequentialCompactness:TheEberlein-mulian
    Theorem
    MemzabilityofWeakTopologies
    16ContinuousLinearOperatorsonHilbertSpaces
    TheInnerProductandOrthogonality
    TheDualSpaceandWeakSequentialConvergence
    BessersInequalityandOrthonormalBases
    bAdjointsandSymmetryforLinearOperators
    CompactOperators
    TheHilbert-SchmidtTheorem
    TheRiesz-SchauderTheorem:CharacterizationofFredholmOperators
    MeasureandIntegration:GeneralTheory
    17GeneralMeasureSpaces:TheirPropertlesandConstruction
    MeasuresandMeasurableSets
    SignedMeasures:TheHahnandJordanDecompositions
    TheCaratheodoryMeasureInducedbyanOuterMeasure
    18IntegrationOeneralMeasureSpaces
    19GengralLSpaces:Completeness,DualityandWeakConvergence
    20TheConstrucitonofParticularMeasures
    21MeasureandTopbogy
    22InvariantMeasures
    Bibiiography
    index
  • 内容简介:
    《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。
  • 目录:
    LebesgueIntegrationforFunctionsofaSingleRealVariable
    PreliminariesonSets,Mappings,andRelations
    UnionsandIntersectionsofSets
    EquivalenceRelations,theAxiomofChoice,andZorn'sLemma
    1TheRealNumbers:Sets.Sequences,andFunctions
    TheField,Positivity,andCompletenessAxioms
    TheNaturalandRationalNumbers
    CountableandUncountableSets
    OpenSets,ClosedSets,andBorelSetsofRealNumbers
    SequencesofRealNumbers
    ContinuousReal-ValuedFunctionsofaRealVariable
    2LebesgneMeasure
    Introduction
    LebesgueOuterMeasure
    Theo'-AlgebraofLebesgueMeasurableSets
    OuterandInnerApproximationofLebesgueMeasurableSets
    CountableAdditivity,Continuity,andtheBorel-CantelliLemma
    NoumeasurableSets
    TheCantorSetandtheCantorLebesgueFunction
    3LebesgReMeasurableFunctions
    Sums,Products,andCompositions
    SequentialPointwiseLimitsandSimpleApproximation
    Littlewood'sThreePrinciples,Egoroff'sTheorem,andLusin'sTheorem
    4LebesgueIntegration
    TheRiemannIntegral
    TheLebesgueIntegralofaBoundedMeasurableFunctionoveraSetof
    FiniteMeasure
    TheLebesgueIntegralofaMeasurableNonnegativeFunction
    TheGeneralLebesgueIntegral
    CountableAdditivityandContinuityofIntegration
    UniformIntegrability:TheVifaliConvergenceTheorem
    viiiContents
    5LebusgueIntegration:Fm'therTopics
    UniformIntegrabilityandTightness:AGeneralVitaliConvergenceTheorem
    ConvergenceinMeasure
    CharacterizationsofRiemaunandLebesgueIntegrability
    6DifferentiationandIntegration
    ContinuityofMonotoneFunctions
    DifferentiabilityofMonotoneFunctions:Lebesgue'sTheorem
    FunctionsofBoundedVariation:Jordan'sTheorem
    AbsolutelyContinuousFunctions
    IntegratingDerivatives:DifferentiatingIndefiniteIntegrals
    ConvexFunction
    7TheLpSpaces:CompletenessandAppro~umation
    Nor/nedLinearSpaces
    TheInequalitiesofYoung,HOlder,andMinkowski
    LvIsComplete:TheRiesz-FiseherTheorem
    ApproximationandSeparability
    8TheLPSpacescDeailtyandWeakConvergence
    TheRieszRepresentationfortheDualof
    WeakSequentialConvergenceinLv
    WeakSequentialCompactness
    TheMinimizationofConvexFunctionals
    IIAbstractSpaces:Metric,Topological,Banach,andHiibertSpaces
    9.MetricSpaces:GeneralProperties
    ExamplesofMetricSpaces
    OpenSets,ClosedSets,andConvergentSequences
    ContinuousMappingsBetweenMetricSpaces
    CompleteMetricSpaces
    CompactMetricSpaces
    SeparableMetricSpaces
    10MetricSpaces:ThreeFundamentalThanreess
    TheArzelb.-AscoliTheorem
    TheBaireCategoryTheorem
    TheBanaehContractionPrinciple
    HTopologicalSpaces:GeneralProperties
    OpenSets,ClosedSets,Bases,andSubbases
    TheSeparationProperties
    CountabilityandSeparability
    ContinuousMappingsBetweenTopologicalSpaces

    CompactTopologicalSpaces
    ConnectedTopologicalSpaces
    12TopologicalSpaces:ThreeFundamentalTheorems
    Urysohn'sLemmaandtheTietzeExtensionTheorem
    TheTychonoffProductTheorem
    TheStone-WeierstrassTheorem
    13ContinuousLinearOperatorsBetweenBauschSpaces
    NormedLinearSpaces
    LinearOperators
    CompactnessLost:InfiniteDimensionalNormodLinearSpaces
    TheOpenMappingandClosedGraphTheorems
    TheUniformBoundednessPrinciple
    14DualityforNormedIinearSpaces
    LinearFtmctionals,BoundedLinearFunctionals,andWeakTopologies
    TheHahn-BanachTheorem
    ReflexiveBanachSpacesandWeakSequentialConvergence
    LocallyConvexTopologicalVectorSpaces
    TheSeparationofConvexSetsandMazur'sTheorem
    TheKrein-MiimanTheorem
    15CompactnessRegained:TheWeakTopology
    Alaoglu'sExtensionofHelley'sTheorem
    ReflexivityandWeakCompactness:Kakutani'sTheorem
    CompactnessandWeakSequentialCompactness:TheEberlein-mulian
    Theorem
    MemzabilityofWeakTopologies
    16ContinuousLinearOperatorsonHilbertSpaces
    TheInnerProductandOrthogonality
    TheDualSpaceandWeakSequentialConvergence
    BessersInequalityandOrthonormalBases
    bAdjointsandSymmetryforLinearOperators
    CompactOperators
    TheHilbert-SchmidtTheorem
    TheRiesz-SchauderTheorem:CharacterizationofFredholmOperators
    MeasureandIntegration:GeneralTheory
    17GeneralMeasureSpaces:TheirPropertlesandConstruction
    MeasuresandMeasurableSets
    SignedMeasures:TheHahnandJordanDecompositions
    TheCaratheodoryMeasureInducedbyanOuterMeasure
    18IntegrationOeneralMeasureSpaces
    19GengralLSpaces:Completeness,DualityandWeakConvergence
    20TheConstrucitonofParticularMeasures
    21MeasureandTopbogy
    22InvariantMeasures
    Bibiiography
    index
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