测度论

图书标准信息

• 作者 [德]霍尔姆斯 著
• 出版社 世界图书出版公司
• 出版时间 2007-02
• 版次 1
• ISBN 9787506282741
• 定价 39.00元
• 装帧 平装
• 开本 32开
• 纸张 胶版纸
• 页数 304页

【内容简介】

　　Mymainpurposeinthisbookistopresentaunifiedtreatmentofthatpartofmeasuretheorywhichinrecentyearshasshownitselftobemostusefulforitsapplicationsinmodernanalysis.IfIhaveaccomplishedmypurpose，thenthebookshouldbefoundusablebothasatextforstudentsandasasourceofreferenceforthemoreadvancedmathematician.
　　Ihavetriedtokeeptoaminimumtheamountofnewandunusualterminologyandnotation.Inthefewplaceswheremynomenclaturediffersfromthatintheexistingliteratureofmeasuretheory，Iwasmotivatedbyanattempttoharmonizewiththeusageofotherpartsofmathematics.Thereare，forinstance，soundalgebraicreasonsforusingtheterms"lattice"and"ring"forcertainclassesofsets--reasonswhicharemorecogentthanthesimilaritiesthatcausedHausdorfftouse"ring"and"field."

【目录】

Preface
Acknowledgments
SECTION
0.Prerequisites
CHAPTERⅠ:SETSANDCLASSES
1.Setinclusion
2.Unionsandintersections
3.Limits,complements,anddifferences
4.Ringsandalgebras
5.Generatedringsanda-rings
6.Monotoneclasses
CHAPTERⅡ:MEASURESANDOUTERMEASURES
7.Measureonrings
8.Measureonintervals
9.Propertiesofmeasures
10.Outermeasures
11.Measurablesets
CHAPTERⅢ:EXTENSIONOFMEASURES
12.Propertiesofinducedmeasures
13.Extension,completion,andapproximation
14.Innermeasures
15Lebesguemeasure
16.Nonmeasurablesets
CHAPTERⅣ:MEASURABLEFUNCTIONS
17.Measurespaces
18.Measurablefunctions
19.Combinationsofmeasurabiefunctions
20.Sequencesofmeasurablefunctions
21.Fointwiseconvergence
22.Convergenceinmeasure
CHAPTERⅤ:INTEGRATION
23.Integrab]eslmp~efunctions
24.Sequencesofintegrablesimplefunctions
25.Integrablefunctions
26.Sequencesofintegrablefunctions
27.Propertiesofintegrals
CHApTEIⅥ:GENERALSETfUNCTIOnS
28.Signedmeasures
29.Hahnandjordandecomposltions
30.Absolutecontinuity
31.TheRadon-Nikodymtheorem
32.Derlwtivesofsignedmeasures
CHAPTERⅦ:PRODUCTSPACES
33.Carteslanproducts
34.Sections
35.Productmeasures
36.Fubinistheorem
37.Finitedimensionalproductspaces
38.Infinitedimensionalproductspaces
CHAPTERⅧ:TRANSFOEMATIONSANDFUNCTION$
39.Measurabletransformations
40.Measurerings
41.Theisomorphismtheorem
42.Functionspaces
43.Setfunctionsandpointfunctions
CHAPTEKⅨ:PROBABILITY
44.Heurlstieintroduction
45.Independence
46.Seriesofindependentfunctions
……
CHAPTERⅩ:LOCALLYCOMPACTSPACES
CHAPTERⅪ:HAARMEALURS
CHAPTERⅫ:MEASUREANDTOPOLOGYINGROUPS
References
Bibliography
Listoffrequentlyusedsymbols
Index