| 书目名称 | Measure and Category | | 副标题 | A Survey of the Anal | | 编辑 | John C. Oxtoby | | 视频video | | | 丛书名称 | Graduate Texts in Mathematics | | 图书封面 |  | | 描述 | 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. A knowledge of calculus is presupposed, and some familiarity with the algebra of sets. The questions discussed are ones that lend themselves naturally to set-theoretical formulation. The book is intended as an introduction to this kind of analysis. It could be used to supplement a standard course in real analysis, as the basis for a seminar, or for inde pendent study. It is primarily expository, but a few refineme | | 出版日期 | Textbook 19711st edition | | 关键词 | calculus | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4615-9964-7 | | isbn_ebook | 978-1-4615-9964-7Series ISSN 0072-5285 Series E-ISSN 2197-5612 | | issn_series | 0072-5285 | | copyright | Springer-Verlag New York 1971 |
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发表于 2025-3-21 16:25:55
