Measure Theory, Integration, and Hilbert Spaces Bk. 3
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Real Analysis by Elias M. Stein
Book DescriptionReal Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidian spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis. The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises. As with the other volumes in the series, Real Analysis is accessible to students interested in such diverse disciplines as mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels. Also available, the first two volumes in the Princeton Lectures in Analysis:
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Book DetailsISBN: 9780691113869
(229mm x 152mm x 32mm)
Imprint: Princeton University Press
Publisher: Princeton University Press
Publish Date: 14-Mar-2005
Country of Publication: United States
Books By Author Elias M. Stein
Lectures on Pseudo-Differential Operators: Regularity Theorems and Applications to Non-Elliptic Problems, Paperback (February 2015)
Functional Analysis, Hardback (September 2008)» View all books by Elias M. Stein
Beginning with the basic facts of functional analysis, this title looks at Banach spaces, Lp spaces, and distribution theory, and highlights their roles in harmonic analysis. It uses the Baire category theorem to illustrate several points, including the existence of Besicovitch sets.
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Author Biography - Elias M. Stein
Elias M. Stein is Professor of Mathematics at Princeton University. Rami Shakarchi received his Ph.D. in Mathematics from Princeton University in 2002.
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