实分析和概率论

图书标准信息

• 作者 [美]达德利（Dudley,R.M.） 著
• 出版社 机械工业出版社
• 出版时间 2006-07
• 版次 1
• ISBN 9787111193487
• 定价 69.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 555页

【内容简介】

《实分析和概率论（英文版）（第2版）》是一本广受称赞的教科书，清晰地讲解了现代概率论以及度量空间与概率测度之间的相互作用。本书分两部分，第一部分介绍了实分析的内容，包括基本集合论、一般拓扑学、测度论、积分法、巴拿赫空间和拓扑空间中的泛函分析导论、凸集和函数、拓扑空间上的测度等。第二部分介绍了基于测度论的概率方面的内容，包括大数律、遍历定理、中心极限定理、条件期望、鞅收敛等。另外，随机过程一章（第12章）还介绍了布朗运动和布朗桥。
与前版相比，本版内容更完善，一开始就介绍了实数系的基础和泛代数中的一致逼近的斯通-魏尔斯特拉斯定理；修订和改进了几节的内容，扩充了大量历史注记；增加了很多新的习题，以及对一些习题的解答的提示。

【作者简介】

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【目录】

PrefacetotheCambridgeEdition
1Foundations;SetTheory
1.1DefinitionsforSetTheoryandtheRealNumberSystem
1.2RelationsandOrderings
*1.3TransfiniteInductionandRecursion
1.4Cardinality
1.5TheAxiomofChoiceandItsEquivalents
2GeneralTopology
2.1Topologies，Metrics，andContinuity
2.2CompactnessandProductTopologies
2.3CompleteandCompactMetricSpaces
2.4SomeMetricsforFunctionSpaces
2.5CompletionandCompletenessofMetricSpaces
*2.6ExtensionofContinuousFunctions
*2.7UniformitiesandUniformSpaces
*2.8Compactification
3Measures
3.1IntroductiontoMeasures
3.2SemiringsandRings
3.3CompletionofMeasures
3.4LebesgueMeasureandNonmeasurableSets
*3.5AtomicandNonatomicMeasures
4Integration
4.1SimpleFunctions
*4.2Measurability
4.3ConvergenceTheoremsforIntegrals
4.4ProductMeasures
*4.5Daniell-StoneIntegrals
5LpSpaces;IntroductiontoFunctionalAnalysis
5.1InequalitiesforIntegrals
5.2NormsandCompletenessofLP
5.3HilbertSpaces
5.40rthonormalSetsandBases
5.5LinearFormsonHilbertSpaces，InclusionsofLPSpaces，
andRelationsBetweenTwoMeasures
5.6SignedMeasures
6ConvexSetsandDualityofNormedSpaces
6.1Lipschitz，Continuous，andBoundedFunctionals
6.2ConvexSetsandTheirSeparation
6.3ConvexFunctions
*6.4DualityofLpSpaces
6.5UniformBoundednessandClosedGraphs
*6.6TheBmnn-MinkowskiInequality
7Measure，Topology，andDifferentiation，
7.1BaireandBorelo-AlgebrasandRegularityofMeasures
*7.2LebesguesDifferentiationTheorems
*7.3TheRegularityExtension
*7.4TheDualofC(K）andFourierSeries
*7.5AlmostUniformConvergenceandLusinsTheorem
8IntroductiontoProbabilityTheory
8.1BasicDefinitions
8.2InfiniteProductsofProbabilitySpaces
8.3LawsofLargeNumbers
*8.4ErgodicTheorems
9ConvergenceofLawsandCentralLimitTheorems
9.1DistributionFunctionsandDensities
9.2ConvergenceofRandomVariables
9.3ConvergenceofLaws
9.4CharacteristicFunctions
9.5UniquenessofCharacteristicFunctions
andaCentralLimitTheorem
9.6TriangularArraysandLindebergsTheorem
9.7SumsofIndependentRealRandomVariables
*9.8TheLevyContinuityTheorem;InfinitelyDivisible
andStableLaws
10ConditionalExpectationsandMartingales
10.1ConditionalExpectations
10.2RegularConditionalProbabilitiesandJensens
Inequality
10.3Martingales
10.4OptionalStoppingandUniformIntegrability
10.5ConvergenceofMartingalesandSubmartingales
*10.6ReversedMartingalesandSubmartingales
*10.7SubadditiveandSuperadditiveErgodicTheorems
11ConvergenceofLawsonSeparableMetricSpaces
11.1LawsandTheirConvergence
11.2LipschitzFunctions
11.3MetricsforConvergenceofLaws
11.4ConvergenceofEmpiricalMeasures
11.5TightnessandUniformTightness
*11.6StrassensTheorem:NearbyVariables
WithNearbyLaws
*11.7AUniformityforLawsandAlmostSurelyConverging
RealizationsofConvergingLaws
*11.8Kantorovich-RubinsteinTheorems
*11.9U-Statistics
12StochasticProcesses
12.1ExistenceofProcessesandBrownianMotion
12.2TheStrongMarkovPropertyofBrownianMotion
12.3ReflectionPrinciples，TheBrownianBridge，
andLawsofSuprema
12.4LawsofBrownianMotionatMarkovTimes:
SkorohodImbedding
12.5LawsoftheIteratedLogarithm
13Measurability:BorelIsomorphismandAnalyticSets
*13.1BorelIsomorphism
*13.2AnalyticSets
AppendixAAxiomaticSetTheory
A.1MathematicalLogic
A.2AxiomsforSetTheory
A.3OrdinalsandCardinals
A.4FromSetstoNumbers
AppendixBComplexNumbers，VectorSpaces，
andTaylorsTheoremwithRemainder
AppendixCTheProblemofMeasure
AppendixDRearrangingSumsofNonnegativeTerms
AppendixEPathologiesofCompactNonmetricSpaces
AuthorIndex
SubjectIndex
NotationIndex