Real Analysis: Modern Techniques and Their ApplicationsJohn Wiley & Sons, 11 juin 2013 - 416 pages An in-depth look at real analysis and its applications-now expanded and revised. This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory. This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include: * Revised material on the n-dimensional Lebesgue integral. * An improved proof of Tychonoff's theorem. * Expanded material on Fourier analysis. * A newly written chapter devoted to distributions and differential equations. * Updated material on Hausdorff dimension and fractal dimension. |
Table des matières
Radon Measures | |
Elements of Fourier Analysis | |
Elements of Distribution Theory | |
Topics in Probability Theory | |
More Measures and Integrals | |
Bibliography | |
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Expressions et termes fréquents
absolutely continuous algebra Banach space Borel measure Borel set bounded called Cauchy closed sets compact Hausdorff space compact sets compact subset compactification complete complex measure contains continuous function Corollary countable define denote dense derivatives differential distribution dominated convergence theorem equivalent example exists f is continuous follows Fourier transform function f ƒ ƒ Haar measure Hausdorff space hence Hilbert space implies inequality intersection intervals isomorphism LCH space Lebesgue measure Lemma linear functional linear map locally compact measurable function measure space metric space Moreover neighborhood nonempty nonnegative normed vector space notation open sets outer measure pointwise polynomial Proof Proposition prove Radon measure random variables regular result satisfies semifinite seminorms sequence signed measure simple functions subspace supp(f Suppose theory topological space topology unique weak