| 词条 | 测度与范畴学 |
| 释义 | 图书信息出版社: 世界图书出版公司; 第2版 (2009年4月1日) 外文书名: Measure and Category (2nd Edition) 平装: 106页 正文语种: 英语 开本: 24 ISBN: 751000439X, 9787510004391 条形码: 9787510004391 尺寸: 21.6 x 14.6 x 0.6 cm 重量: 159 g 作者简介作者：(美国) 奥凯斯屠拜 (Oxtoby.J.C.) 内容简介《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 |
| 随便看 |
百科全书收录4421916条中文百科知识，基本涵盖了大多数领域的百科知识，是一部内容开放、自由的电子版百科全书。