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，作者在遍历理论、代数逻辑、算子理论等方面的研究很有成就。书中全面论述了测度论的各个方面，介绍了前苏联和法国个学派的研究工作及其重要成果。

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，作者在遍历理论、代数逻辑、算子理论等方面的研究很有成就。书中全面论述了测度论的各个方面，介绍了前苏联和法国个学派的研究工作及其重要成果。详细内容包括了：集合与类，测度和外测度，测度的扩张，测度函数，积分，一般集合函数，积空间，变换和函数，概率论，局部紧空间，Huar测度，群中的测度和拓扑。本书适用于数学专业的研究生及科研人员。

Preface  

Acknowledgments

O．Prerequisites 

CHAPTER I：SETS AND CLASSES

1. Set inclusion          

2. Unions and intersections        

3. Limits，complements，and differences

4. Ringsg and algebras

5. Generated rings and 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 setsn       

CHAPTER IV：MEASURABLE FUNCTIONS

17．Measure space 

18．Measurable functions

19．Combinations of measurable functions

20．Sequences of measurable functions 

21．Pointwise convergence

22．Convergenceinmeasure    

CHAPTER V：INTEGRATI0N

23. Integrable simple functions    

24. Sequences of integrable simple functions

25. Integrable functions    

26. Sequences of integrable functions  

27. Properdes ofintegrals    

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

CHAPTERVII：PRODUCT SPACES

33. Cartesian products     

34. Sections       

35. Product measures    

36. Fubini’s theorem     

37. Finite dimensional product spaces

38. Infinite 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

46． Series ofindependent functions

47． The law oflarge numbers       

48． Conditional probabilities and expectations

49． Measures on product spaces   

CHAPTER X：LOCALLY COMPACT SPACES

50． Topological 1emmas         

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． Well topology         

63． Quotient groups          

64． The regularity of Haar measure     

References            

Bibliography    

List of frequently used symbolsn 

Index