实分析（英文）

图书标准信息

• 作者 [美]斯坦恩（Stein E.M.） 著
• 出版社 世界图书出版公司
• 出版时间 2013-01
• 版次 1
• ISBN 9787510040535
• 定价 59.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 402页
• 正文语种 英语

【内容简介】

　　《实分析（英文）》在Princeton大学使用，同时在其它学校，比如UCLA等名校也在本科生教学中得到使用。其教学目的是，用统一的、联系的观点来把现代分析的“核心”内容教给本科生，力图使本科生的分析学课程能接上现代数学研究的脉络。

【目录】

Foreword
Introduction
1Fourierseries：completion
2Limitsofcontinuousfunctions
3Lengthofcurves
4Differentiationandintegration
5Theproblemofmeasure

Chapter1.MeasureTheory
1Prelhninaries
2Theexteriormeasure
3MeasurablesetsandtheLebesguemeasure
4Measurablefunctions
4.1Definitionandbasicproperties
4.2Approximationbysimplefunctionsorstepfunctions
4.3Littlewood'sthreeprinciples
5TheBrunn-Minkowskiinequality
6Exercises
7Problems

Chapter2.IntegrationTheory
1TheLebesgueintegral：basicpropertiesandconvergencetheorems
2ThespaceL1ofintegrablefunctions
3Fubini'stheorem
3.1Statementandproofofthetheorem
3.2ApplicationsofFubini'stheorem
4*AFourierinversionformula
5Exercises
6Problems

Chapter3.DifferentiationandIntegration
1Differentiationoftheintegral
1.1TheHardy-Littlewoodmaximalfunction
1.2TheLebesguedifferentiationtheorem
2Goodkernelsandapproximationstotheidentity
3Differentiabilityoffunctions
3.1Functionsofboundedvariation
3.2Absolutelycontinuousfunctions
3.3Differentiabilityofjumpfunctions
4Rectifiablecurvesandtheisoperimetricinequality
4.1Minkowskicontentofacurve
4.2Isoperimetricinequality
5Exercises
6Problems

Chapter4.HilbertSpaces：AnIntroduction
1TheHilbertspaceL2
2Hilbertspaces
2.1Orthogonality
2.2Unitarymappings
2.3Pre-Hilbertspaces
3FourierseriesandFatou'stheorem
3.1Fatou'stheorem
4Closedsubspacesandorthogonalprojections
5Lineartransformations
5.1LinearfunctionalsandtheRieszrepresentationtheorem
5.2Adjoints
5.3Examples
6Compactoperators
7Exercises
8Problems

Chapter5.HilbertSpaces：SeveralExamples
1TheFouriertransformonL2
2TheHardyspaceoftheupperhalf-plane
3Constantcoefficientpartialdifferentialequations
3.1Weaaksolutions
3.2Themaintheoremandkeyestimate
4TheDirichletprinciple
4.1Harmonicfunctions
4.2TheboundaryvalueproblemandDirichlet'sprinciple
5Exercises
6Problems

Chapter6.AbstractMeasureandIntegrationTheory
Chapter7.HausdorffMeasureandFractals
NotesandReferences
Bibliography
SymbolGlossary
Index