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Real Analysis: A Comprehensive Course in Analysis, Part 1, by Barry Simon
Fee Download Real Analysis: A Comprehensive Course in Analysis, Part 1, by Barry Simon
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A Comprehensive Course in Analysis by Poincare Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 1 is devoted to real analysis. From one point of view, it presents the infinitesimal calculus of the twentieth century with the ultimate integral calculus (measure theory) and the ultimate differential calculus (distribution theory). From another, it shows the triumph of abstract spaces: topological spaces, Banach and Hilbert spaces, measure spaces, Riesz spaces, Polish spaces, locally convex spaces, Frechet spaces, Schwartz space, and $L^p$ spaces. Finally it is the study of big techniques, including the Fourier series and transform, dual spaces, the Baire category, fixed point theorems, probability ideas, and Hausdorff dimension. Applications include the constructions of nowhere differentiable functions, Brownian motion, space-filling curves, solutions of the moment problem, Haar measure, and equilibrium measures in potential theory.
- Sales Rank: #1165303 in Books
- Published on: 2015-11-02
- Original language: English
- Dimensions: 10.00" h x 7.00" w x 1.75" l, 3.45 pounds
- Binding: Hardcover
- 789 pages
About the Author
Barry Simon, California Institute of Technology, Pasadena, CA, USA.
Most helpful customer reviews
14 of 15 people found the following review helpful.
Minor Notes
By Christopher Grant
Obviously, this and the other 4 volumes in the series are fated to become classic texts for higher-level analysis. Some few of you may be curious about the rate of errata for 3000+ pages of newly-printed math. Here's what I've found after finishing the first chapter:
1) In the Preface, Niels Bohr is called "Neils".
2) The definition of a well-ordered set on Page 10 neglects to mention that it is only *nonempty* subsets that require a smallest element.
3) We are told specifically that Z_+ and C_+ exclude 0, but we don't seem to be told about R_+. If it also excludes 0, then the statement on Pages 10 and 11 that every (nonempty?) subset of R_+ has an infimum would seem to fail.
4) On Page 16, Aleph_{n+1} is mischaracterized as being equal to 2^{Aleph_n} (as if the GCH were assumed true).
5) In formula (1.7.3) on Page 18, x_ell should be y_ell.
6) In the proof of Proposition 1.7.2 on Page 20, X and W are mixed up with x and w.
7) In the second paragraph of the proof of Proposition 1.7.7 on Page 23, projection operators seem to lose their subscripts.
8) In the sketch of the proof of Theorem 1.8.4 on Page 32, "sup" should be "supp".
9) "Bounded sequence on increasing reals" (p. 16), "is group homomorphism" (p. 18), and "finite linear combination are dense" (p. 18) were probably not meant to read exactly that way.
Some few of you might also wonder about the physical construction of the books in the series. They are similar to recent books in the GSM series: non-glossy, pure-white paper with sewn bindings.
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