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Synopsis
This self-contained treatment of measure and integration begins with a brief review of the Riemann integral and proceeds to a construction of Lebesgue measure on the real line. From there the reader is led to the general notion of measure, to the construction of the Lebesgue integral on a measure space, and to the major limit theorems, such as the Monotone and Dominated Convergence Theorems. The treatment proceeds to $L^p$ spaces, normed linear spaces that are shown to be complete (i.e., Banach spaces) due to the limit theorems. Particular attention is paid to $L^2$ spaces as Hilbert spaces, with a useful geometrical structure.
Having gotten quickly to the heart of the matter, the text proceeds to broaden its scope. There are further constructions of measures, including Lebesgue measure on $n$-dimensional Euclidean space. There are also discussions of surface measure, and more generally of Riemannian manifolds and the measures they inherit, and an appendix on the integration of differential forms. Further geometric aspects are explored in a chapter on Hausdorff measure. The text also treats probabilistic concepts, in chapters on ergodic theory, probability spaces and random variables, Wiener measure and Brownian motion, and martingales.
This text will prepare graduate students for more advanced studies in functional analysis, harmonic analysis, stochastic analysis, and geometric measure theory.
"synopsis" may belong to another edition of this title.
Review
"Taylor's treatment throughout is elegant and very efficient ... I found reading the text very enjoyable." ---- MAA Reviews
"The book is very understandable, requiring only a basic knowledge of analysis. It can be warmly recommended to a broad spectrum of readers, to graduate students as well as young researchers." ---- EMS Newsletter
"This monograph provides a quite comprehensive presentation of measure and integration theory and of some of their applications." ---- Mathematical Reviews
"About this title" may belong to another edition of this title.
- PublisherAmerican Mathematical Society
- Publication date2006
- ISBN 10 0821841807
- ISBN 13 9780821841808
- BindingHardcover
- LanguageEnglish
- Number of pages319
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Measure Theory and Integration (Graduate Studies in Mathematics)
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Measure Theory and Integration (Graduate Studies in Mathematics)
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Measure Theory and Integration - Graduate Studies in Mathematics Volume 76 (Graduate Studies in Mathematics)
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Measure Theory and Integration
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Measure Theory and Integration
Published by
American Mathematical Society, 2006
ISBN 10: 0821841807
ISBN 13: 9780821841808
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Measure Theory and Integration (Hardcover)
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ISBN 10: 0821841807
ISBN 13: 9780821841808
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Hardcover. Condition: new. Hardcover. This self-contained treatment of measure and integration begins with a brief review of the Riemann integral and proceeds to a construction of Lebesgue measure on the real line. From there the reader is led to the general notion of measure, to the construction of the Lebesgue integral on a measure space, and to the major limit theorems, such as the Monotone and Dominated Convergence Theorems. The treatment proceeds to $L^p$ spaces, normed linear spaces that are shown to be complete (i.e., Banach spaces) due to the limit theorems. Particular attention is paid to $L^2$ spaces as Hilbert spaces, with a useful geometrical structure. Having gotten quickly to the heart of the matter, the text proceeds to broaden its scope.There are further constructions of measures, including Lebesgue measure on $n$-dimensional Euclidean space. There are also discussions of surface measure, and more generally of Riemannian manifolds and the measures they inherit, and an appendix on the integration of differential forms. Further geometric aspects are explored in a chapter on Hausdorff measure. The text also treats probabilistic concepts, in chapters on ergodic theory, probability spaces and random variables, Wiener measure and Brownian motion, and martingales. This text will prepare graduate students for more advanced studies in functional analysis, harmonic analysis, stochastic analysis, and geometric measure theory. Offers a treatment of measure and integration that begins with a brief review of the Riemann integral and proceeds to a construction of Lebesgue measure on the real line. This text also treats probabilistic concepts, in chapters on ergodic theory, probability spaces and random variables, Wiener measure and Brownian motion, and martingales. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780821841808
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Measure Theory and Integration
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Measure Theory and Integration
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ISBN 13: 9780821841808
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Measure Theory and Integration
Published by
American Mathematical Society, 2006
ISBN 10: 0821841807
ISBN 13: 9780821841808
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Measure Theory and Integration (Graduate Studies in Mathematics)
Published by
American Mathematical Society, 2006
ISBN 10: 0821841807
ISBN 13: 9780821841808
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Condition: New. Offers a treatment of measure and integration that begins with a brief review of the Riemann integral and proceeds to a construction of Lebesgue measure on the real line. This text also treats probabilistic concepts, in chapters on ergodic theory, probability spaces and random variables, Wiener measure and Brownian motion, and martingales. Series: Graduate Studies in Mathematics. Num Pages: 319 pages, Illustrations. BIC Classification: PB. Category: (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Weight in Grams: 765. . 2006. Hardcover. . . . . Seller Inventory # V9780821841808
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