测度与范畴学 pdf epub mobi txt 电子书下载 2025

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出版者:世界图书出版公司

作者:（美）奥凯斯屠拜（Oxtoby,J.C）

出品人:

页数:106 页

译者:

出版时间:2009-4

价格:18.00元

装帧:

isbn号码:9787510004391

丛书系列:Graduate Texts in Mathematics

图书标签:

数学
GTM
实分析
实分析7
测度
拓扑学
math
QS

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《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

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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