测度论（影印版）

　　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."本书为英文版。

暂缺《测度论（影印版）》作者简介

Preface
Acknowledgments
SECTION
0.Prerequisites
CHAPTERI:SETSANDCLASSES
1.Setinclusion
2.Unionsandintersections
3.Limits,complements,anddifferences
4.Ringsandalgebras
5.Generatedringsand-rings
6.Monotoneclasses
CHAPTERII:MEASURESANDOUTERMEASUR.ES
7.Measureonrings
8.Measureonintervals
9.Propertiesofmeasures
10.Outermeasures
11.Measurablesets
CHAPTERIII:EXTENSION'OFMEASURES
12.Propertiesofinducedmeasures
13.Extension,completion,andapproximation
14.Innermeasures
15.Lebesguemeasure
16.Nonmeasurablesets
CHAPTERIV:MEASURABLEFUNCTIONS
17.Measurespaces
18.Measurablefunctions
19.Combinationsofmeasurablefunctions
20.Sequencesofmeasurablefunctions
21.Pointwlseconvergence
22.Convergenceinmeasure
CHAPTERV:INTEGRATION
23.Integrablesimplefunctions
24.Sequencesofintegrablesimplefunctions
25.Integrablefunctions
26.Sequencesofintegrablefunctions
27.Propertiesofintegrals
CHAPTERVI:GENERALSETFUNCTIONS
28.Signedmeasures
29.HahnandJordandecompositions
30.Absolutecontinuity
31.TheRadon-Nikodymtheorem
32.Derivativesofsignedmeasures
CHAPTERVII:PRODUCTSPACES
33.Cartesianproducts
34.Sections
35.Productmeasures
36.Fubini'stheorem
37.Finitedimensionalproductspaces
38.Infinitedimensionalproductspaces
CHAPTERVIII:TRANSFORMATIONSANDFUNCTIONS
39.Measurabletransformations
40.Measurerings
41.Theisomorphismtheorem
42.Functionspaces
43.Setfunctionsandpointfunctions
CHAPTERIX:PROBABILITY
44.Heuristicintroduction
45.Independence
46.Seriesofindependentfunctions
47.Thelawoflargenumbers
48.Conditionalprobabilitiesandexpectations
49.Measuresonproductspaces
CHAPTERX:LOCALLYCOMPACTSPACES
50.Topologicallemmas
51.BorelsetsandBairesets
52.Regularmeasures
53.GenerationofBorelmeasures
54.Regularcontents
55.Classesofcontinuousfunctions
56.Linearfunctionals
CHAPTERXI:HAARMEASURE
57.Fullsubgroups
58.Existence
59.Measurablegroups
60.Uniqueness
CHAPTERXII:MEASUREANDTOPOLOGYINGROUPS
61.Topologyintermsofmeasure
62.Weiltopology
63.Quotientgroups
64.TheregularityofHaarmeasure
References
Bibliography
Listoffrequentlyusedsymbols
Index