实分析原理

图书标准信息

• 作者 [美]阿里普兰蒂斯（Aliprantis,C.D） 著
• 出版社 世界图书出版公司
• 出版时间 2009-01
• 版次 1
• ISBN 9787506292726
• 定价 49.00元
• 装帧 平装
• 开本 32开
• 纸张 胶版纸
• 页数 415页
• 正文语种 英语

【内容简介】

　　ThisisthethirdeditionofPrinciplesofRealAlysis,firstpublishedin1981.Theaimofthiseditionistoaccommodatethecurrentneedsforthetraditionalrealanalysiscoursethatisusuallytakenbytheseniorundergraduateorbythefirstyeargraduatestudentinmathematics.Thiseditiondifferssubstantiallyfromthesecondedition.Eachchapterhasbeengreatlyimprovedbyincorporatingnewmaterialandbyrearrangingtheoldmaterial.Moreover,anewchapter（Chapter6）onHilbertspacesandFourieranalysishasbeenadded.

【目录】

Preface
CHAPTER1.FUNDAMENTALSOFREALANALYSIS
1.ElementarySetTheory
2.CountableandUncountableSets
3.TheRealNumbers
4.SequencesofRealNumbers
5.TheExtendedRealNumbers
6.MetricSpaces
7.CompactnessinMetricSpaces

CHAPTER2.TOPOLOGYANDCONTINUITY
8.TopologicalSpaces
9.ContinuousReal-ValuedFunctions
10.SeparationPropertiesofContinuousFunctions
11.TheStone-WeierstrassApproximationTheorem

CHAPTER3.THETHEORYOFMEASURE
12.SemiringsandAlgebrasofSets
13.MeasuresonSemirings
14.OuterMeasuresandMeasurableSets
15.TheOuterMeasureGeneratedbyaMeasure
16.MeasurableFunctions
17.SimpleandStepFunctions
18.TheLebesgueMeasure
19.ConvergenceinMeasure
20.AbstractMeasurability

CHAPTER4.THELEBESGUEINTEGRAL
21.UpperFunctions
22.IntegrableFunctions
23.TheRiemannIntegralasaLebesgueIntegral
24.ApplicationsoftheLebesgueIntegral
25.ApproximatingIntegrableFunctions
26.ProductMeasuresandIteratedIntegrals

CHAPTER5.NORMEDSPACESANDLp-SPACES
27.NormedSpacesandBanachSpaces
28.OperatorsBetweenBanachSpaces
29.LinearFunctionals
30.BanachLattices
31.Lp-Spaces

CHAPTER6.HILBERTSPACES
32.InnerProductSpaces
33.HilbertSpaces
34.OrthonormalBases
35.FourierAnalysis

CHAPTER7.SPECIALTOPICSININTEGRATION
36.SignedMeasures
37.ComparingMeasuresandthe
Radon-NikodymTheorem
38.TheRieszRepresentationTheorem
39.DifferentiationandIntegration
40.TheChangeofVariablesFormula
Bibliography
ListofSymbols
Index