正版现货 书 测度论（英文影印版） [美] Paul R.Halmos（P.R.哈尔莫斯） 著 世图科技 世界图书出版公司
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9787519255848
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ISBN:
9787519255848
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出版时间:
2015-01
上书时间2024-05-01
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名称：书 测度论（英文影印版） [美] Paul R.Halmos（P.R.哈尔莫斯） 著 世图科技 世界图书出版公司
作者：佚名
品相：全新
出版时间：2015-01
装订：平装
ISBN：9787519255848
出版社：世界图书出版公司
商品描述：
作者Halmos在遍历理论、代数逻辑、算子理论等方面的研究很有成就。本书是Springer《数学研究生教材》丛书之１８卷，是测度论的经典名著，书中对测度论作了较全面的论述，并详细介绍了前苏联和法国各学派的研究工作及其重要成果。 本书作者Paul R. Halmos是美国印第安纳大学（Indiana University）数学系教授，曾获得肖维纳奖（Chauvenet Prize） 和 斯蒂尔奖（Steele Prize ）等多个奖项。 Preface Acknowledgments 0. Prerequisites CHAPTER Ⅰ:SETS AND CLASSES 1.Set inclusion 2.Unions and intersections 3.Limits， complements， and differences 4.Rings and algebras 5.Generated rings and σ-rings 6.Monotone classes CHAPTER Ⅱ:MEASURES AND OUTER MEASURES 7.Measure on rings 8.Measure on intervals 9.Properties of measures 10.Outer measures 11.Measurable sets CHAPTER Ⅲ:EXTENSION OF MEASURES 12.Properties of induced measures 13.Extension， completion， and approximation 14.Inner measures 15.Lebesgue measure 16.Non measurable sets CHAPTER Ⅳ:MEASUKABLE FUNCTIONS 17.Measure spaces 18.Measurable functions 19.Combinations of measurable functions 20.Sequences of measurable functions 21.Pointwise convergence 22.Convergence in measure CHAPTER Ⅴ:INTEGRATION 23.Integrable simple functions 24.Sequences of integrablc simple functions 25.Integrable Functions 26.Sequences of intcgrablc functions 27.Properties of integrals CHAPTER Ⅵ:GENERAL SET FUNCTIONS 28.Signed measures 29.Hahn and Jordan decompositions 30.Absolute continuity 31.The Radon-Nikodym theorem 32.Derivatives of signed measures CHAPTER Ⅶ:PRODUCT SPACES 33.Cartesian products 34.Sections 35.Product measures 36.Fubini's theorem 37.Finite dimensional product spaces 38.Infinitc dimensional product spaces CHAPTER Ⅷ:TRANSFORMATIONS AND FUNCTIONS 39.Measurable transformations 40.Measure rings 41.The isomorphism theorem 42.Function spaces 43.Set functions and point functions CHAPTER Ⅸ:PROBABILITY 44.Heuristic introduction 45.Independence 45.Series of independent functions 47.The law of large numbers 48.Conditional probabilities and expectations 49.Measures on product spaces CHAPTER Ⅹ: LOCALLY COMPACT SPACES 50.Topological lemmas 51.Borel sets and Baire sets 52.Regular measures 53.Generation of Borel measures 54.Regular contents 55.Classes of continuous functions 56.Linear functionals CHAPTER Ⅺ: HAAR MEASURE 57.Full subgroups 58.Existence 59.Measurable groups 60.Uniqueness CHAPTER Ⅻ: MEASURE AND TOPOLOGY IN GROUPS 61.Topology in terms of measure 62.Weil topology 63.Quotient groups 64.The regularity of Haar measure References Bibliography List of frequently used symbols Index '
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