Real analysis: modern techniques and their applications

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Wiley, 24/mar/1999 - 386 pagine
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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.

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Review: Real Analysis: Modern Techniques and Their Applications

Recensione dell'utente  - DJ - Goodreads

likely text for math 525a Leggi recensione completa

Review: Real Analysis: Modern Techniques and Their Applications

Recensione dell'utente  - Pietro - Goodreads

Read the measure/integration part. Not much motivation or intuition, but good job with the choice of axiomatic development (very abstract from the outset). Terrific exercises. Leggi recensione completa

Indice

Prologue
1
Measures 79
19
Integration
43
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Informazioni sull'autore (1999)

GERALD B. FOLLAND is Professor of Mathematics at the University of Washington in Seattle. He has written extensively on mathematical analysis, including Fourier analysis, harmonic analysis, and differential equations.

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