| 书目名称 | Real Analysis | | 编辑 | Peter A Loeb | | 视频video | | | 概述 | Written by one of the leading scholars in the field.Includes a novel presentation of differentiation and absolute continuity using a local maximum function, resulting in an exposition that is both sim | | 图书封面 |  | | 描述 | This textbook is designed for a year-long course in real analysis taken by beginning graduate and advanced undergraduate students in mathematics and other areas such as statistics, engineering, and economics. Written by one of the leading scholars in the field, it elegantly explores the core concepts in real analysis and introduces new, accessible methods for both students and instructors..The first half of the book develops both Lebesgue measure and, with essentially no additional work for the student, general Borel measures for the real line. Notation indicates when a result holds only for Lebesgue measure. Differentiation and absolute continuity are presented using a local maximal function, resulting in an exposition that is both simpler and more general than the traditional approach..The second half deals with general measures and functional analysis, including Hilbert spaces, Fourier series, and the Riesz representation theorem for positive linear functionals on continuous functions with compact support. To correctly discuss weak limits of measures, one needs the notion of a topological space rather than just a metric space, so general topology is introduced in terms of a base | | 出版日期 | Textbook 2016 | | 关键词 | Real analysis; Riemann Integral; Lebesgue measure; Hilbert spaces; Banach Spaces | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-319-30744-2 | | isbn_softcover | 978-3-319-80879-6 | | isbn_ebook | 978-3-319-30744-2 | | copyright | Springer International Publishing Switzerland 2016 |
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发表于 2025-3-21 19:02:09
