测度与范畴学

图书标准信息

• 作者 奥凯斯屠拜（Oxtoby.J.C.） 著
• 出版社 世界图书出版公司
• 出版时间 2009-04
• 版次 2
• ISBN 9787510004391
• 定价 18.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 106页
• 正文语种 英语

【内容简介】

Thisbookhastwomainthemes：theBairecategorytheoremasamethodforprovingexistence,andthe"duality"betweenmeasureandcategory.Thecategorymethodisillustratedbyavarietyoftypicalapplications,andtheanalogybetweenmeasureandcategoryisexploredinallofitsramifications.Tothisend,theelementsofmetrictopologyarereviewedandtheprincipalpropertiesofLebesguemeasurearederived.ItturnsoutthatLebesgueintegrationisnotessentialforpresentpurposes——theRiemannintegralissufficient.Conceptsofgeneralmeasuretheoryandtopologyareintroduced,butnotjustforthesakeofgenerality.Needlesstosay,theterm"category"refersalwaystoBairecategory;ithasnothingtodowiththetermasitisusedinhomologicalalgebra

【目录】

1.MeasureandCategoryontheLine
2.LiouvilleNumbers
3.LebesgueMeasureinr-Space
4.ThePropertyofBaire
5.Non-MeasurableSets
6.TheBanach-MazurGame
7.FunctionsofFirstClass
8.TheTheoremsofLusinandEgoroff
9.MetricandTopologicalSpaces
10.ExamplesofMetricSpaces
11.NowhereDifferentiableFunctions
12.TheTheoremofAlexandroff
13.TransformingLinearSetsintoNullsets
14.Fubini'sTheorem
15.TheKuratowski-UlamTheorem
16.TheBanachCategoryTheorem
17.ThePoincareRecurrenceTheorem
18.TransitiveTransformations
19.TheSierpinski-ErdosDualityTheorem
20.ExamplesofDuality
21.TheExtendedPrincipleofDuality
22.CategoryMeasureSpaces
SupplementaryNotesandRemarks
References
SupplementaryReferences
Index