测度论

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。

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

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。

暂无其它内容！

暂时还没有人为这本书评论！