欧氏空间上的勒贝格积分（修订版）（英文版）

图书标准信息

• 作者 琼斯（Frank Jones） 著
• 出版社 世界图书出版公司
• 出版时间 2010-01
• 版次 1
• ISBN 9787510005558
• 定价 79.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 588页
• 正文语种 英语

【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