欧氏空间上的勒贝格积分(修订版)(英文版)

欧氏空间上的勒贝格积分(修订版)(英文版)
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作者: (Frank Jones)
2010-01
版次: 1
ISBN: 9787510005558
定价: 79.00
装帧: 平装
开本: 24开
纸张: 胶版纸
页数: 588页
正文语种: 英语
分类: 自然科学
62人买过
  •   《欧氏空间上的勒贝格积分(修订版)(英文版)》简明、详细地介绍勒贝格测度和Rn上的积分。《欧氏空间上的勒贝格积分(英文版)》的基本目的有四个,介绍勒贝格积分;从一开始引入n维空间;彻底介绍傅里叶积分;深入讲述实分析。贯穿全书的大量练习可以增强读者对知识的理解。目次:Rn导论;Rn勒贝格测度;勒贝格积分的不变性;一些有趣的集合;集合代数和可测函数;积分;Rn勒贝格积分;Rn的Fubini定理;Gamma函数;Lp空间;抽象测度的乘积;卷积;Rn+上的傅里叶变换;单变量傅里叶积分;微分;R上函数的微分。
      读者对象:《欧氏空间上的勒贝格积分(修订版)(英文版)》适用于数学专业的学生、老师和相关的科研人员。 Preface
    Bibliography
    Acknowledgments
    1IntroductiontoRn
    ASets
    BCountableSets
    CTopology
    DCompactSets
    EContinuity
    FTheDistanceFunction

    2LebesgueMeasureonRn
    AConstruction
    BPropertiesofLebesgueMeasure
    CAppendix:ProofofP1andP2

    3InvarianceofLebesgueMeasure
    ASomeLinearAlgebra
    BTranslationandDilation
    COrthogonalMatrices
    DTheGeneralMatrix

    4SomeInterestingSets
    AANonmeasurableSet
    BABevyofCantorSets
    CTheLebesgueFunction
    DAppendix:TheModulusofContinuityoftheLebesgueFunctions

    5AlgebrasofSetsandMeasurableFunctions
    AAlgebrasanda-Algebras
    BBorelSets
    CAMeasurableSetwhichIsNotaBorelSet
    DMeasurableFunctions
    ESimpleFunctions

    6Integration
    ANonnegativeFunctions
    BGeneralMeasurableFunctions
    CAlmostEverywhere
    DIntegrationOverSubsetsofRn
    EGeneralization:MeasureSpaces
    FSomeCalculations
    GMiscellany

    7LebesgueIntegralonRn
    ARiemannIntegral
    BLinearChangeofVariables
    CApproximationofFunctionsinL1
    DContinuityofTranslationinL1

    8FubinisTheoremforRn
    9TheGammaFunction
    ADefinitionandSimpleProperties
    BGeneralization
    CTheMeasureofBalls
    DFurtherPropertiesoftheGammaFunction
    EStirlingsFormula
    FTheGammaFunctiononR

    10LPSpaces,
    ADefinitionandBasicInequalities
    BMetricSpacesandNormedSpaces
    CCompletenessofLp
    DTheCasep=∞
    ERelationsbetweenLpSpaces
    FApproximationbyC∞c(Rn)
    GMiscellaneousProblems;
    HTheCase0[p[1

    11ProductsofAbstractMeasures
    AProductsof5-Algebras
    BMonotoneClasses
    CConstructionoftheProductMeasure
    DTheFubiniTheorem
    ETheGeneralizedMinkowskiInequality

    12Convolutions
    AFormalProperties
    BBasicInequalities
    CApproximateIdentities

    13FourierTransformonRn
    AFourierTransformofFunctionsinL1(Rn)
    BTheInversionTheorem
    CTheSchwartzClass
    DTheFourier-PlancherelTransform
    EHilbertSpace
    FFormalApplicationtoDifferentialEquations
    GBesselFunctions
    HSpecialResultsforn=i
    IHermitePolynomials

    14FourierSeriesinOneVariable
    APeriodicFunctions
    BTrigonometricSeries
    CFourierCoefficients
    DConvergenceofFourierSeries
    ESummabilityofFourierSeries
    FACounterexample
    GParsevalsIdentity
    HPoissonSummationFormula
    IASpecialClassofSineSeries

    15Differentiation
    ATheVitaliCoveringTheorem
    BTheHardy-LittlewoodMaximalFunction
    CLebesguesDifferentiationTheorem
    DTheLebesgueSetofaFunction
    EPointsofDensity
    FApplications
    GTheVitaliCoveringTheorem(Again)
    HTheBesicovitchCoveringTheorem
    ITheLebesgueSetofOrderp
    JChangeofVariables
    KNoninvertibleMappings

    16DifferentiationforFunctionsonR
    AMonotoneFunctions
    BJumpFunctions
    CAnotherTheoremofFubini
    DBoundedVariation
    EAbsoluteContinuity
    FFurtherDiscussionofAbsoluteContinuity
    GArcLength
    HNowhereDifferentiableFunctions
    IConvexFunctions
    Index
    SymbolIndex
  • 内容简介:
      《欧氏空间上的勒贝格积分(修订版)(英文版)》简明、详细地介绍勒贝格测度和Rn上的积分。《欧氏空间上的勒贝格积分(英文版)》的基本目的有四个,介绍勒贝格积分;从一开始引入n维空间;彻底介绍傅里叶积分;深入讲述实分析。贯穿全书的大量练习可以增强读者对知识的理解。目次:Rn导论;Rn勒贝格测度;勒贝格积分的不变性;一些有趣的集合;集合代数和可测函数;积分;Rn勒贝格积分;Rn的Fubini定理;Gamma函数;Lp空间;抽象测度的乘积;卷积;Rn+上的傅里叶变换;单变量傅里叶积分;微分;R上函数的微分。
      读者对象:《欧氏空间上的勒贝格积分(修订版)(英文版)》适用于数学专业的学生、老师和相关的科研人员。
  • 目录:
    Preface
    Bibliography
    Acknowledgments
    1IntroductiontoRn
    ASets
    BCountableSets
    CTopology
    DCompactSets
    EContinuity
    FTheDistanceFunction

    2LebesgueMeasureonRn
    AConstruction
    BPropertiesofLebesgueMeasure
    CAppendix:ProofofP1andP2

    3InvarianceofLebesgueMeasure
    ASomeLinearAlgebra
    BTranslationandDilation
    COrthogonalMatrices
    DTheGeneralMatrix

    4SomeInterestingSets
    AANonmeasurableSet
    BABevyofCantorSets
    CTheLebesgueFunction
    DAppendix:TheModulusofContinuityoftheLebesgueFunctions

    5AlgebrasofSetsandMeasurableFunctions
    AAlgebrasanda-Algebras
    BBorelSets
    CAMeasurableSetwhichIsNotaBorelSet
    DMeasurableFunctions
    ESimpleFunctions

    6Integration
    ANonnegativeFunctions
    BGeneralMeasurableFunctions
    CAlmostEverywhere
    DIntegrationOverSubsetsofRn
    EGeneralization:MeasureSpaces
    FSomeCalculations
    GMiscellany

    7LebesgueIntegralonRn
    ARiemannIntegral
    BLinearChangeofVariables
    CApproximationofFunctionsinL1
    DContinuityofTranslationinL1

    8FubinisTheoremforRn
    9TheGammaFunction
    ADefinitionandSimpleProperties
    BGeneralization
    CTheMeasureofBalls
    DFurtherPropertiesoftheGammaFunction
    EStirlingsFormula
    FTheGammaFunctiononR

    10LPSpaces,
    ADefinitionandBasicInequalities
    BMetricSpacesandNormedSpaces
    CCompletenessofLp
    DTheCasep=∞
    ERelationsbetweenLpSpaces
    FApproximationbyC∞c(Rn)
    GMiscellaneousProblems;
    HTheCase0[p[1

    11ProductsofAbstractMeasures
    AProductsof5-Algebras
    BMonotoneClasses
    CConstructionoftheProductMeasure
    DTheFubiniTheorem
    ETheGeneralizedMinkowskiInequality

    12Convolutions
    AFormalProperties
    BBasicInequalities
    CApproximateIdentities

    13FourierTransformonRn
    AFourierTransformofFunctionsinL1(Rn)
    BTheInversionTheorem
    CTheSchwartzClass
    DTheFourier-PlancherelTransform
    EHilbertSpace
    FFormalApplicationtoDifferentialEquations
    GBesselFunctions
    HSpecialResultsforn=i
    IHermitePolynomials

    14FourierSeriesinOneVariable
    APeriodicFunctions
    BTrigonometricSeries
    CFourierCoefficients
    DConvergenceofFourierSeries
    ESummabilityofFourierSeries
    FACounterexample
    GParsevalsIdentity
    HPoissonSummationFormula
    IASpecialClassofSineSeries

    15Differentiation
    ATheVitaliCoveringTheorem
    BTheHardy-LittlewoodMaximalFunction
    CLebesguesDifferentiationTheorem
    DTheLebesgueSetofaFunction
    EPointsofDensity
    FApplications
    GTheVitaliCoveringTheorem(Again)
    HTheBesicovitchCoveringTheorem
    ITheLebesgueSetofOrderp
    JChangeofVariables
    KNoninvertibleMappings

    16DifferentiationforFunctionsonR
    AMonotoneFunctions
    BJumpFunctions
    CAnotherTheoremofFubini
    DBoundedVariation
    EAbsoluteContinuity
    FFurtherDiscussionofAbsoluteContinuity
    GArcLength
    HNowhereDifferentiableFunctions
    IConvexFunctions
    Index
    SymbolIndex
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