## Real analysis: modern techniques and their applicationsAn 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. |

### Dall'interno del libro

90 pagine corrispondenti a **folland real analysis** in questo libro

#### Pagina iv

#### Pagina 368

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#### Review: Real Analysis: Modern Techniques and Their Applications

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### Parole e frasi comuni

a-algebra a-finite absolutely continuous algebra Banach space Borel measure Borel set bounded called Cauchy Cc(X closed sets compact Hausdorff space compact sets compact subset compactification complete contains continuous functions Corollary countable cr-algebra define definition denote dense derivatives differential disjoint union distribution dominated convergence theorem E C X equivalent example exists finite measure follows Fourier transform Haar measure Hausdorff space hence implies inequality intersection intervals isomorphic LCH space Lebesgue measure Lemma linear functional linear map locally compact measurable function measure space metric space monotone convergence theorem Moreover neighborhood nonempty nonnegative normed vector space notation obtain open sets outer measure pointwise polynomial Proposition prove Radon measure random variables result satisfies seminorms sequence signed measure simple functions subspace supp Suppose theory topological space topology uniformly unique