圖書信息
出版社: 世界圖書出版公司; 第2版 (2009年4月1日)
外文書名: Measure and Category (2nd Edition)
平裝: 106頁
正文語種: 英語
開本: 24
ISBN: 751000439X, 9787510004391
條形碼: 9787510004391
尺寸: 21.6 x 14.6 x 0.6 cm
重量: 159 g
作者簡介
作者：(美國) 奧凱斯屠拜 (Oxtoby.J.C.)
內容簡介
《測度與範疇學(第2版)》講述了：This book has two main Themes: the Baire category theorem as a method for proving existence, and the "duality" between measure and category. The category method is illustrated by a variety of typical applications, and the analogy between measure and category is explored in all of its ramifications. To this end, the elements of metric topology are reviewed and the principal properties of Lebesgue measure are derived. It turns out that Lebesgue integration is not essential for present purposes——the Riemann integral is sufficient. Concepts of general measure theory and topology are introduced, but not just for the sake of generality. Needless to say, the term "category" refers always to Baire category; it has nothing to do with the term as it is used in homological algebra
目錄
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
