《测度与范畴学(第2版)》讲述了：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
目录
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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
