測度論

內(nèi)容概要

本書是Springer《數(shù)學(xué)研究生教材》叢書之18卷，是測度論的經(jīng)典名著，作者在遍歷理論、代數(shù)邏輯、算子理論等方面的研究很有成就。書中全面論述了測度論的各個(gè)方面，介紹了前蘇聯(lián)和法國各學(xué)派的研究工作及其重要成果。詳細(xì)內(nèi)容包括：集合與類；測度和外測度；測度的擴(kuò)張；測度函數(shù)；積分；一般集合函數(shù)；積空間；變換和函數(shù)；概率；局部緊空間；Huar測度；群中的測度和拓?fù)?。本書適用于數(shù)學(xué)專業(yè)的研究生及科研人員。

書籍目錄

PrefaceAcknowledgmentsSECTION0.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 classesCHAPTER Ⅱ: MEASURES AND OUTER MEASURES  7. Measure on rings  8. Measure on intervals  9. Properties of measures  10. Outer measures  11. Measurable setsCHAPTER Ⅲ: EXTENSION OF MEASURES  12. Properties of induced measures  13. Extension, completion, and approximation  14. Inner measures  15 Lebesgue measure  16. Non measurable setsCHAPTER Ⅳ: MEASURABLE FUNCTIONS  17. Measure spaces  18. Measurable functions  19. Combinations ofmeasurabie functions  20. Sequences of measurable functions  21. Fointwise convergence  22. Convergence in measureCHAPTER Ⅴ: INTEGRATION  23. Integrab]e slmp~e functions  24. Sequences of integrable simple functions  25. Integrable functions  26. Sequences ofintegrable functions  27. Properties of integralsCHApTEI Ⅵ: GENERAL SET fUNCTIOnS  28. Signed measures  29. Hahn and jordan decomposltions  30. Absolute continuity  31. The Radon-Nikodym theorem  32. Derlwtives of signed measuresCHAPTER Ⅶ: PRODUCT SPACES  33. Carteslan products  34. Sections  35. Product measures  36. Fubini's theorem  37. Finite dimensional product spaces  38. Infinite dimensional product spacesCHAPTER Ⅷ: TRANSFOEMATIONS AND FUNCTION$  39. Measurable transformations  40. Measure rings  41. The isomorphism theorem  42. Function spaces  43. Set functions and point functionsCHAPTEK Ⅸ: PROBABILITY  44. Heurlstie introduction  45. Independence  46. Series of independent functions ……CHAPTER Ⅹ:LOCALLY COMPACT SPACESCHAPTER Ⅺ:HAAR MEALURSCHAPTER Ⅻ:MEASURE AND TOPOLOGY IN GROUPSReferencesBibliographyList of frequently used symbolsIndex

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