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1、ConvexGeometricAnalysisMSRIPublicationsVolume34,1998ContentsIntroduction:TheConvexGeometryandGeometricAnalysisProgram,MSRI,Spring1996ixProgramSeminarsxiGAFASeminars1994–1996xixIntegralsofSmoothandAnalyticFunctionsoverMinkowski’sSumsofConvexSets1SemyonAle
2、skerLocalizationTechniqueontheSphereandtheGromov–MilmanTheoremontheConcentrationPhenomenononUniformlyConvexSphere17SemyonAleskerGeometricInequalitiesinOptionPricing29ChristerBorellRandomPointsinIsotropicConvexSets53JeanBourgainThresholdIntervalsunderGrou
3、pSymmetries59JeanBourgainandGilKalaiOnaGeneralizationoftheBusemann–PettyProblem65JeanBourgainandGaoyongZhangIsotropicConstantsofSchattenClassSpaces77SeanDarOntheStabilityoftheVolumeRadius81EfimD.GluskinPolytopeApproximationsoftheUnitBallof`n89pW.TimothyG
4、owersARemarkabouttheScalar-Plus-CompactProblem111W.TimothyGowersviiviiiCONTENTSAnotherLow-TechnologyEstimateinConvexGeometry117GregKuperbergOntheEquivalenceBetweenGeometricandArithmeticMeansforLog-ConcaveMeasures123RafalLatalaOntheConstantintheReverseBru
5、nn–MinkowskiInequalityforp-ConvexBalls129AlexanderE.LitvakTheExtensionoftheFinite-DimensionalVersionofKrivine’sTheoremtoQuasi-NormedSpaces139AlexanderE.LitvakANoteonGowers’DichotomyTheorem149BernardMaureyAn“Isomorphic”VersionofDvoretzky’sTheorem,II159Vit
6、aliMilmanandGideonSchechtmanAsymptoticVersionsofOperatorsandOperatorIdeals165VitaliMilmanandRoyWagnerMetricEntropyoftheGrassmannManifold181AlainPajorCurvatureofNonlocalMarkovGenerators189MichaelSchmuckenschlager?AnExtremalPropertyoftheRegularSimplex199Mi
7、chaelSchmuckenschlager?FloatingBody,IlluminationBody,andPolytopalApproximation203CarstenSchutt?ANoteontheM¤-LimitingConvolutionBody231AntonisTsolomitisConvexGeometricAnalysisMSRIPublicationsVolume34,1998IntegralsofSmoothandAnalyticFunctionsoverMinkowski’
8、sSumsofConvexSetsSEMYONALESKER1.IntroductionandStatementofMainResultsLetKˉ=(K;K;:::;K)beans-tupleofcompactconvexsubsetsofRn.12sForanycontinuousfunctionF:Rn?!C,considerthefunctionMssKˉF:R+?!C;whereR+=f(?1;:::;?s)j?j?0g;de?n
