测度论（英文版） measure theory

图书标准信息

• 作者 [美]杜波 著
• 出版社 世界图书出版公司
• 出版时间 2009-06
• 版次 1
• ISBN 9787510004780
• 定价 28.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 210页
• 正文语种 英语

【内容简介】

Inpresentingthistreatmentofhomologicalalgebra，itisapleasuretoacknowledgethehelpandencouragementwhichIhavehadfromallsides.Homologicalalgebraarosefrommanysourcesinalgebraandtopology.Decisiveexamplescamefromthestudyofgroupextensionsandtheirfactorsets，asubjectIlearnedinjointworkwithOTTOSCHIL-LING.Afurtherdevelopmentofhomologicalideas，withaviewtotheirtopologicalapplications，cameinmylongcollaborationwithSAHUELEZLENBERG;tobothcollaborators，especialthanks.FormanyyearstheAirForceOfficeofScientificResearchsupportedmyresearchprojectsonvarioussubjectsnowsummarizedhere;itisapleasuretoacknowledgetheirlivelyunderstandingOfbasicscience.

【作者简介】

　　SaundersMacLanewasbornonAugust4，1909inConnecticut.HestudiedatYaleUniversityandthenattheUniversityofChicagoandatG6ttingen，wherehereceivedtheD.Phil.in1934.HehastaughtatHarvard，Cornel1andtheUniversityofChicago.MacLanesinitialresearchwasinlogicandinalgebraicnumbertheory（valuationtheory）.WithSamuelEilenberghepublishedfifteenpapersonalgebraictopology.Anumberoftheminvolvedtheinitialstepsinthecohomologyofgroupsandinotheraspectsofhomologicalalgebra-aswellasthediscoveryofcategorytheory.HisfamousundergraduatetextbookSurveyofmodernalgebra，writtenjointlywithG.Birkhoff，hasremainedinprintforover50years.MacLaneisalsotheauthorofseveralotherhighlysuccessfulbooks.

【目录】

Introduction
O.ConventionsandNotation
1.Notation:Euclideanspace
2.Operationsinvolving
3.Inequalitiesandinclusions
4.Aspaceanditssubsets
5.Notation:generationofclassesofsets
6.Productsets
7.Dotnotationforanindexset
8.Notation:setsdefinedbyconditionsonfunctions
9.Notation:openandclosedsets
10.Limitofafunctionatapoint
11.Metricspaces
12.Standardmetricspacetheorems
13.Pseudometricspaces
I.OperationsonSets
I.Unionsandintersections
2.Thesymmetricdifferenceoperator
3.Limitoperationsonsetsequences
4.Probabilisticinterpretationofsetsandoperationsonthem
II.ClassesofSubsetsofaSpace
1.Setalgebras
2.Examples
3.Thegenerationofsetalgebras
4.TheBorelsetsofametricspace
5.Productsofsetalgebras
6.Monotoneclassesofsets
III.SetFunctions
1.Setfunctiondefinitions
2.Extensionofafinitelyadditivesetfunction
3.Productsofsetfunctions
4.Heuristicsonaalgebrasandintegration
5.Measuresandintegralsonacountablespace
6.Independenceandconditionalprobability(preliminarydiscussion)
7.Dependenceexamples
8.Inferiorandsuperiorlimitsofsequencesofmeasurablesets
9.Mathematicalcounterpartsofcointossing
10.Setwiseconvergenceofmeasuresequences
11.Outermeasure
12.OutermeasuresofcountablesubsetsofR
13.Distanceonasetalgebradefinedbyasubadditivesetfunction
14.Thepseudometricspacedefinedbyanoutermeasure
15.Nonadditivesetfunctions
IV.MeasureSpaces
1.Completionofameasurespace(S,$,~,)
2.GeneralizationoflengthonR
3.Ageneralextensionproblem
4.Extensionofameasuredefinedonasetalgebra
5.ApplicationtoBorelmeasures
6.StrengtheningofTheorem5whenthemetricspaceSiscompleteandseparable
7.Continuitypropertiesofmonotonefunctions
8.ThecorrespondencebetweenmonotoneincreasingfunctionsonRandmeasuresonB(R)
9.DiscreteandcontinuousdistributionsonR
10.Lebesgue-StieltjesmeasuresonR/vandtheircorrespondingmonotonefunctions
11.Productmeasures
12.ExamplesofmeasuresonRN
13.Marginalmeasures
14.Cointossing
15.TheCaratheodorymeasurabilitycriterion
16.Measurehulls
V.MeasurableFunctions
1.Functionmeasurability
2.Functionmeasurabilityproperties
3.Measurabilityandsequentialconvergence
4.Bairefunctions
5.Jointdistributions
6.Measuresonfunction(coordinate)space
……
VI.Intezration
VII.HilbertSoace
VIII.ConvergenceofMeasureSequences
IX.SignedMeasures
X.MeasuresandFunctionsofBoundedVariationonR
XI.ConditionalExpectations;MartingaleTheory
Notation
Index