成功加入购物车
页面干净无破损无字迹
[德] 阿莫恩 著 / 世界图书出版公司 / 2012-09 / 平装
售价 ¥ 200.00
品相 九五品
优惠 满包邮
延迟发货说明
上书时间2024-03-07
卖家超过10天未登录
分析(第3卷)
Thisthirdvolumeconcludesourintroductiontoanalysis,whereinwefinishlayingthegroundworkneededforfurtherstudyofthesubject.Aswiththefirsttwo,thisvolumecontainsmorematerialthancantreatedinasinglecourse.Itisthereforeimportantinpreparinglecturestochooseasuitablesubsetofitscontent;theremaindercanbetreatedinseminarsorlefttoindependentstudy.Foraquickoverviewofthiscontent,consultthetableofcontentsandthechapterintroductions.
ForewordChapterⅨElementsofmeasuretheory1Measurablespacesσ-algebrasTheBorelσ-algebraThesecondcountabilityaxiomGeneratingtheBorela-algebrawithintervalsBasesoftopologicalspacesTheproducttopologyProductBorela-algebrasMeasurabilityofsections2MeasuresSetfunctionsMeasurespacesPropertiesofmeasuresNullsetsOutermeasuresTheconstructionofoutermeasuresTheLebesgueoutermeasureTheLebesgue-StieltjesoutermeasureHausdorffoutermeasures4MeasurablesetsMotivationThea-algebraof/μ*-measurablesetsLebesguemeasureandHausdorffmeasureMetricmeasures5TheLebasguemeasureTheLebesguemeasurespaceTheLebesguemeasureisregularAcharacterizationofLebesguemeasurabilityImagesofLebesguemeasurablesetsTheLebesguemeasureistranslationinvariantAcharacterizationofLebesguemeasureTheLebesguemeasureisinvariantunderrigidmotionsThesubstitutionruleforlinearmapsSetswithoutLebesguemeasureChapterⅩIntegrationtheory1MeasurablefunctionsSimplefunctionsandmeasurablefunctionsAmeasurabilitycriterionMeasurableR-valuedfunctionsThelatticeofmeasurableT-valuedfunctionsPointwiselimitsofmensurablefunctionsRadonmeasures2IntegrablefuuctionsTheintegralofasimplefunctionTheL1-seminormTheBochner-LebesgueintegralThecompletenessofL1ElementarypropertiesofintegralsConvergenceinL13ConvergencetheoremsIntegrationofnonnegativeT-valuedfunctionsThemonotoneconvergencetheoremFatou'slemmaIntegrationofR-valuedfunctionsLebesgue'sdominatedconvergencetheoremParametrizedintegrals4LebesguespacesEssentiallyboundedfunctionsTheHolderandMinkowskiinequalitiesLebesguespacesarecompleteLp-spacesContinuousfunctionswithcompactsupportEmbeddingsContinuouslinearfunctionalsonLp5Then-dimensionalBochner-LebesgueintegralLebesguemeasurespacesTheLebesgueintegralofabsolutelyintegrablefunctionsAcharacterizationofRiemannintegrablefunctions6Fubiul'stheoremMapsdefinedalmosteverywhereCavalieri'sprincipleApplicationsofCavalieri'sprincipleTonelli'stheoremFubini'stheoremforscalarfunctionsFubini'stheoremforvector-vainedfunctionsMinkowski'sinequalityforintegralsAcharacterizationofLp(Rm+n,E)Atracetheorem7TheconvolutionDefiningtheconvolutionThetranslationgroupElementarypropertiesoftheconvolutionApproximationstotheidentityTestfunctionsSmoothpartitionsofunityConvolutionsofE-valuedfunctionsDistributionsLineardifferentialoperatorsWeakderivatives8ThesubstitutionrulePullingbacktheLebesguemeasureThesubstitutionrule:generalcasePlanepolarcoordinatesPolarcoordinatesinhigherdimensionsIntegrationofrotationallysymmetricfunctionsThesubstitutionruleforvector-valuedfunctions9TheFouriertransformDefinitionandelementarypropertiesThespaceofrapidlydecreasingfunctionsTheconvolutionalgebraSCalculationswiththeFouriertransformTheFourierintegraltheoremConvolutionsandtheFouriertransformFouriermultiplicationoperatorsPlancherel'stheoremSymmetricoperatorsTheHeisenberguncertaintyrelationChapterⅪManifoldsanddifferentialforms1SubmanifoldsDefinitionsandelementarypropertiesSubmersionsSubmanifo]dswithboundaryLocalchartsTangentsandnormalsTheregularvaluetheoremOne-dimensionalmanifoldsPartitionsofunity2MultUinearalgebraExteriorproductsPullbacksThevolumeelementTheRieszisomorphismTheHodgestaroperatorIndefiniteinnerproductsTensors3ThelocaltheoryofdifferentialformsDefinitionsandbasisrepresentationsPullbacksTheexteriorderivativeThePoincarelemmaTensors4VectorfieldsanddifferentialformsVectorfieldsLocalbasisrepresentationDifferentialformsLocalrepresentationsCoordinatetransformationsTheexteriorderivativeClosedandexactformsContractionsOrientabilityTensorfields5RiemannianmetricsThevolumeelementRiemannianmanifoldsTheHodgestarThecodifferential6VectoranalysisTheRieszisomorphismThegradientThedivergenceTheLaplace-BeltramioperatorThecurlTheLiederivativeTheHodge-LaplaceoperatorThevectorproductandthecurlChapterⅫIntegrationonmanifolds1VolumemeasureTheLebesguea-algebraofMThedefiaitionofthevolumemeasurePropertiesIntegrabilityCalculationofseveralvolumes2IntegrationofdifferentialformsIntegralsofm-formsRestrictionstosubmanifoldsThetransformationtheoremFubini'stheoremCalculationsofseveralintegralsFlowsofvectorfieldsThetransporttheorem3Stokes'stheoremStokes'stheoremforsmoothmanifoldsManifoldswithsingularitiesStokes'stheoremwithsingularitiesPlanardomainsHigher-dimensionalproblemsHomotopyinvarianceandapplicationsGauss'slawGreen'sformulaTheclassicalStokes'stheoremThestaroperatorandthecoderivativeReferences
展开全部
图2
配送说明
...
相似商品
为你推荐
开播时间:09月02日 10:30