实分析教程（第2版）

图书标准信息

• 作者 [美]麦克唐纳（McDonald J.N.） 著
• 出版社 世界图书出版公司
• 出版时间 2013-01
• 版次 2
• ISBN 9787510052637
• 定价 139.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 667页
• 正文语种 英语

【内容简介】

　　《实分析教程（第2版）》是一部备受专家好评的教科书，书中用现代的方式清晰论述了实分析的概念与理论，定理证明简明易懂，可读性强，全书共有200道例题和1200例习题。《实分析教程（第2版）》的写法像一部文学读物，这在数学教科书很少见，因此阅读《实分析教程（第2版）》会是一种享受。

【作者简介】

　　麦克唐纳（JohnN.McDonald），McDonaldAfterreceivinghisPh.D.inmathematicsfromRutgersUniversity,JohnN.McDonaldjoinedthefacultyintheDepartmentofMathematics（nowtheSchoolofMathematicalandStatisticalScrences）atArizonaStateUniversity,whereheattainedtherankoffullprofessor.McDonaldhastaughtawiderangeofmathematicscourses,includingcalculus,linearalgebra,difFerentialequations,realanalysis,complexanalysis,andfunctionalanalysis.Knownbycolleaguesandstudentsalikeasanexcelientinstructor,McDonaldwashonoredbyhisdepartmentwiththeCharlesWexlerTeachingAward.HealsoservesasamentorintheprestigiousJoaquinBustozMath-SaenceHonorsProgram,anintenseacademicprogramthatpfovidesmotivatedstudentsanopportunitytocommenceuniversitymathematicsandsciencestudiespriortograduatinghighschool.McDonaldhasnumerousresearchpubHcations,whichspantheareasofcomplexanalysistfunctionalanalysis,harmonicanalysis,andprobabilitytheory.HeisalsoaformerManagingFditoroftheRockyMountainJournalofMathematics.McDonaldandhiswife,Pat,havefourchildrenandsixgrandchildren.Inadditiontospendingtimewithhisfamily,heenjoysmusic,film,andstayingphysicallyfitthroughjoggingandotherexercising.

【目录】

AbouttheAuthorsPreface
PARTONE.SetTheory，RealNumbers，andCalculus
1.SETTHEORYBiography：GeorgCantor
1.1BasicDefinitionsandProperties
1.2FunctionsandSets
1.3EquivalenceofSets；Countability
1.4Algebras，a-Algebras，andMonotoneClasses
2.THEREALNUMBERSYSTEMANDCALCULUS
Biography：GeorgFriedrichBernhardRiemann
2.1TheReaINumberSystem
2.2SequencesofRealNumbers
2.3OpenandClosedSets
2.4Real-ValuedFunctions
2.5TheCantorSetandCantorFunction
2.6TheRiemannIntegral

PARTTWO.Measure，Integration，andDifFerentiation
3.LEBESGUEMEASUREONTHEREALLINE
Biography：EmileFelix-Edouard-JustrnBorel
3.1BorelMeasurableFunctionsandBorelSets
3.2LebesgueOuterMeasure
3.3FurtherPropertiesofLebesgueOuterMeasure
3.4LebesgueMeasure
4.THELEBESGUEINTEGRALONTHEREALLINE
Biography：HenriLeonLebesgue
4.1TheLebesgueIntegralforNonnegativeFunctions
4.2ConvergencePropertiesoftheLebesgueIntegralforNonnegativeFunctions
4.3TheGeneralLebesgueIntegral
4.4LebesgueAlmostEverywhere
5.ELEMENTSOFMEASURETHEORY
Biography：ConstantinCaratheodory
5.1MeasureSpaces
5.2MeasurableFunctions
5.3TheAbstractLebesgueIntegralforNonnegativeFunctions
5.4TheGeneralAbstractLebesgueIntegral
5.5ConvergenceinMeasure
6.EXTENSIONSTOMEASURESANDPRODUCTMEASURE
Biography：GuidoFubini
6.1ExtensionstoMeasures
6.2TheLebesgue-StieltjesIntegral
6.3ProductMeasureSpaces
6.4IterationoflntegralsinProductMeasureSpaces
7.ELEMENTSOFPROBABILITY
Biography：AndreiNiko/aewchKolmogorov
7.1TheMathematicalModelforProbability
7.2RandomVariables
7.3ExpectationofRandomVariables
7.4TheLawofLargeNumbers
……

PARTTHREE.Topological，Metric，andNormedSpaces
PARTFOUR.HarmonicAnalysis，DynamicaISystems，andHausdorffMeasure