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 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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