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Real Analysis: Measure Theory, Integration, and Hilbert Spaces: Bk. 3 Hardcover – 14 June 2005

by Elias M. Stein (Author), Rami Shakarchi (Author)
4.8 out of 5 stars 86 ratings
Edition: 1st
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Real 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.

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  1. ISBN-10
    9780691113869
  2. ISBN-13
    978-0691113869
  3. Edition
    1st
  4. Publisher
    Princeton University Press
  5. Publication date
    14 June 2005
  6. Book 2 of 3
    Princeton Lectures in Analysis
  7. Language
    English
  8. Dimensions
    16.51 x 3.18 x 23.5 cm
  9. Print length
    424 pages
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Review


""As one would expect from these authors, the exposition is, in general, excellent. The explanations are clear and concise with many well-focused examples as well as an abundance of exercises, covering the full range of difficulty. . . . [I]t certainly must be on the instructor's bookshelf as a first-rate reference book.""---William P. Ziemer, SIAM Review

About the Author

Elias M. Stein is Professor of Mathematics at Princeton University. Rami Shakarchi received his Ph.D. in Mathematics from Princeton University in 2002.

Product details

  • ASIN ‏ : ‎ 0691113866
  • Publisher ‏ : ‎ Princeton University Press; 1st edition (14 June 2005)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 424 pages
  • ISBN-10 ‏ : ‎ 9780691113869
  • ISBN-13 ‏ : ‎ 978-0691113869
  • Dimensions ‏ : ‎ 16.51 x 3.18 x 23.5 cm
  • Customer Reviews:
    4.8 out of 5 stars 86 ratings

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  1. Rami Shakarchi

    Rami Shakarchi

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4.8 out of 5 stars
86 global ratings

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  • Harold
    5.0 out of 5 stars Pretty clear
    Reviewed in the United States on 8 May 2024
    Verified Purchase
    Great exposition of a difficult topic.
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  • Amazon Customer
    3.0 out of 5 stars Three Stars
    Reviewed in Canada on 12 September 2017
    Verified Purchase
    The book has good quality. However, I received it a week later than expected.
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  • Jonny
    5.0 out of 5 stars Very good
    Reviewed in India on 28 July 2024
    Verified Purchase
    Very good
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  • Amazon Customer
    5.0 out of 5 stars Excellent sourse for graduate analysis
    Reviewed in the United States on 3 July 2005
    Verified Purchase
    This book is the best book on real analysis I have ever studied. It does a wonderful job in bridging undergraduate level with graduate level analysis. I have not seen any book that makes measure and Lebesgue theory so easy to understand.

    The books begins by defining what a "measure" is all about. And the description is so intuitive and geometrical that you would wonder why you weren't taught it this way before. The book then goes into Lebesgue theory and all of it suddenly becomes so easy.

    The book has plenty of wonderful examples and a good set of over 30 problems per chapter.

    Elias Stein (one of the authors) is a very renowned mathematician, and one need not worry about the accuracy of the proofs in the book--they are "bullet-proof", and at the same time succinct.

    If you are struggling with W. Rudin's book on Analysis, this book is a MUST for you.
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  • B
    5.0 out of 5 stars One of the bests in measure theory
    Reviewed in the United States on 4 May 2019
    Verified Purchase
    A masterpiece by Stein. This is a book that everyone who’s interested in measure theory must read. Very on point, very clear, and well written. Goes over all you need to do research or even if you’re a graduate student. Not a very advanced book but talk about whatever you need to understand advanced research areas in mathematics, statistics, and even electrical engineering. Very great book.
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