测度论

Preface

Acknowledgments

SECTION

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 a-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: MEASURABLE FUNCTIONS

17. Measure spaces

18. Measurable functions

19. Combinations ofmeasurabie functions

20. Sequences of measurable functions

21. Fointwise convergence

22. Convergence in measure

CHAPTER Ⅴ: INTEGRATION

23. Integrab]e slmp~e functions

24. Sequences of integrable simple functions

25. Integrable functions

26. Sequences ofintegrable functions

27. Properties of integrals

CHApTEI Ⅵ: GENERAL SET fUNCTIOnS

28. Signed measures

29. Hahn and jordan decomposltions

30. Absolute continuity

31. The Radon-Nikodym theorem

32. Derlwtives of signed measures

CHAPTER Ⅶ: PRODUCT SPACES

33. Carteslan products

34. Sections

35. Product measures

36. Fubinis theorem

37. Finite dimensional product spaces

38. Infinite dimensional product spaces

CHAPTER Ⅷ: TRANSFOEMATIONS AND FUNCTION$

39. Measurable transformations

40. Measure rings

41. The isomorphism theorem

42. Function spaces

43. Set functions and point functions

CHAPTEK Ⅸ: PROBABILITY

44. Heurlstie introduction

45. Independence

46. Series of independent functions

……

CHAPTER Ⅹ:LOCALLY COMPACT SPACES

CHAPTER Ⅺ:HAAR MEALURS

CHAPTER Ⅻ:MEASURE AND TOPOLOGY IN GROUPS

References

Bibliography

List of frequently used symbols

Index

My main purpose in this book is to present a unified treatment of that part of measure theory which in recent years has shown itself to be most useful for its applications in modern analysis. If I have accomplished my purpose， then the book should be found usable both as a text for students and as a source of reference for the more advanced mathematician.
　　I have tried to keep to a minimum the amount of new and unusual terminology and notation. In the few places where my nomenclature differs from that in the existing literature of measure theory， I was motivated by an attempt to harmonize with the usage of other parts of mathematics. There are， for instance， sound algebraic reasons for using the terms "lattice" and "ring" for certain classes of sets--reasons which are more cogent than the similarities that caused Hausdorff to use "ring" and "field."

《测度论》推荐阅读。