Real Analysis: Modern Techniques and Their Applications

ISBN-13: 9780471317166 / Angielski / Twarda / 1999 / 416 str.

Gerald B. (University of Washington) Folland

Opis

Real analysis studies the functions of a real variable, including such areas as measurements and integration and topology. Originally applied to the theory of functions of one and several real variables, real analysis has come to encompass several subjects of a more general and abstract nature that underlie much of modern analysis. These general theories and their applications are the subject of this book.

Spis treści

Measures.

Integration.

Signed Measures and Differentiation.

Point Set Topology.

Elements of Functional Analysis.

L¯p Spaces.

Radon Measures.

Elements of Fourier Analysis.

Elements of Distribution Theory.

Topics in Probability Theory.

More Measures and Integrals.

Bibliography.

Indexes.

O autorze

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.

Blurb

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.