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Titlebook: Real Analysis; Peter A Loeb Textbook 2016 Springer International Publishing Switzerland 2016 Real analysis.Riemann Integral.Lebesgue measu

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樓主
發(fā)表于 2025-3-21 19:02:09 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Real Analysis
編輯Peter A Loeb
視頻videohttp://file.papertrans.cn/823/822124/822124.mp4
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
圖書封面Titlebook: Real Analysis;  Peter A Loeb Textbook 2016 Springer International Publishing Switzerland 2016 Real analysis.Riemann Integral.Lebesgue measu
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
關鍵詞Real analysis; Riemann Integral; Lebesgue measure; Hilbert spaces; Banach Spaces
版次1
doihttps://doi.org/10.1007/978-3-319-30744-2
isbn_softcover978-3-319-80879-6
isbn_ebook978-3-319-30744-2
copyrightSpringer International Publishing Switzerland 2016
The information of publication is updating

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沙發(fā)
發(fā)表于 2025-3-21 21:07:25 | 只看該作者
Measure on the Real Line,e set. Given a finite probability experiment, probabilities are associated with outcomes. Riemann integration associates with each finite interval in the real line, the length of that interval. These are all examples of a “finitely additive measure.”
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發(fā)表于 2025-3-22 07:17:43 | 只看該作者
Hilbert Spaces,ation. To avoid repetition, we will work with the complex case, which will include the real case. That is, for a complex number . (. and . real), the . is .. For a real number ., the conjugate .. Therefore, if the scalar field is just the real numbers, then the conjugation operation . is just the id
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Topological Spaces,play a central role in obtaining results. An open ball with center . and radius .?>?0 is denoted by .(.,?.); it is the set {.?∈?.:?.(.,?.)??0 such that the open ball .(.,?.) is contained in .. If .?∈?.(.,?.), th
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發(fā)表于 2025-3-22 15:14:48 | 只看該作者
Textbook 2016ther 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
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發(fā)表于 2025-3-22 23:43:44 | 只看該作者
Hilbert Spaces,. is .. For a real number ., the conjugate .. Therefore, if the scalar field is just the real numbers, then the conjugation operation . is just the identity operation on .. For this reason, we can treat both the real and complex scalar cases at the same time. Here is the definition of the space.
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