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.
Booknews Covers 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, focus is on measure and integration theory, point set topology, and the basics of functional analysis. Illustrates use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory. This second edition offers material of interest to students outside of pure analysis as well as those interested in dynamical systems. Includes a review of sets and metric spaces, plus chapter exercises. For graduate students. Annotation c. by Book News, Inc., Portland, Or.

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zlib/Mathematics/Analysis/Gerald B. Folland/Real Analysis: Modern Techniques and Their Applications_1063253.pdf

Real Analysis, Vol. 1:Modern Techniques and Their Applications

Folland, Gerald B.

Wiley Imprint ; John Wiley & Sons, Incorporated

Jossey-Bass, Incorporated Publishers

WILEY COMPUTING Publisher

Pure and applied mathematics, Pure and applied mathematics (John Wiley & Sons : Unnumbered), 2nd ed., New York, New York State, 1999

Pure and applied mathematics (John Wiley & Sons. Unnumbered), Second edition, New York, cop. 1999

Pure and Applied Mathematics: a Wiley Series of Texts, Monographs and Tracts Ser

John Wiley & Sons, Inc., Hoboken, N.J., 2013

United States, United States of America

2nd, PS, 2007

до 2011-08

lg624078

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类型: 图书

丛书名: Pure and Applied Mathematics: a Wiley Series of Texts, Monographs and Tracts Ser

出版社: Wiley Imprint ; John Wiley & Sons, Incorporated

页码: 408

开本: USD 173.00

价格: 23.600x16.500 cm

出版日期: 1999.04

出版社: Wiley-Interscience

开本: $140.00

价格: 9.3 x 6.3 x 1 inches

出版社: Wiley

Includes bibliographical references (p. 365-375) and index.
"A Wiley-Interscience publication."

Cover......Page 1
Title......Page 2
Copyright Page......Page 3
Preface......Page 5
Contents......Page 8
0.1 The Language of Set Theory......Page 14
0.2 Orderings......Page 17
0.3 Cardinality......Page 19
0.4 More about Well Ordered Sets......Page 22
0.5 The Extended Real Number System......Page 23
0.6 Metric Spaces......Page 26
0.7 Notes and References......Page 29
1.1 Introduction......Page 32
1.2 a-algebras......Page 34
1.3 Measures......Page 37
1.4 Outer Measures......Page 41
1.5 Borel Measures on the Real Line......Page 46
1.6 Notes and References......Page 53
2.1 Measurable Functions......Page 56
2.2 Integration of Nonnegative Functions......Page 62
2.3 Integration of Complex Functions......Page 65
2.4 Modes of Convergence......Page 73
2.5 Product Measures......Page 77
2.6 Then-dimensional Lebesgue Integral......Page 83
2.7 Integration in Polar Coordinates......Page 90
2.8 Notes and References......Page 94
3.1 Signed Measures......Page 98
3.2 The Lebesgue-Radon-Nikodym Theorem......Page 101
3.3 Complex Measures......Page 106
3.4 Diferentiation on Euclidean Space......Page 108
3.5 Functions of Bounded Variation......Page 113
3.6 Notes and References......Page 122
4.1 Topological Spaces......Page 126
4.2 Continuous Maps......Page 132
4.3 Nets......Page 138
4.4 Compact Spaces......Page 141
4.5 Locally Compact Hausdorff Spaces......Page 144
4.6 Two Compactness Theorems......Page 149
4.7 The Stone-Weierstrass Theorem......Page 151
4.8 Embeddings in Cubes......Page 156
4.9 Notes and References......Page 159
5.1 Normed Vector Spaces......Page 164
5.2 Linear Functionals......Page 170
5.3 The Baire Category Theorem and its Consequences......Page 174
5.4 Topological Vector Spaces......Page 178
5.5 Hilbert Spaces......Page 184
5.6 Notes and References......Page 192
6.1 Basic Theory of L^p Spaces......Page 194
6.2 The Dual of L^p......Page 201
6.3 Some Useful Inequalities......Page 206
6.4 Distribution Functions and Weak L^p......Page 210
6.5 Interpolation of L^p Spaces......Page 213
6.6 Notes and References......Page 221
7.1 Positive Linear Functionals on C_c(X)......Page 224
7.2 Regularity and Approximation Theorems......Page 229
7.3 The Dual of C_0(X)......Page 234
7.4 Products of Radon Measures......Page 239
7.5 Notes and References......Page 244
8.1 Preliminaries......Page 248
8.2 Convolutions......Page 252
8.3 The Fourier Transform......Page 260
8.4 Summation of Fourier Integrals and Series......Page 270
8.5 Pointwise Convergence of Fourier Series......Page 276
8.6 Fourier Analysis of Measures......Page 283
8.7 Applications to Partial Diferential Equations......Page 286
8.8 Notes and References......Page 291
9.1 Distributions......Page 294
9.2 Compactly Supported, Tempered, and Periodic Distributions......Page 304
9.3 Sobolev Spaces......Page 314
9.4 Notes and References......Page 323
10.1 Basic Concepts......Page 326
10.2 The Law of Large Numbers......Page 333
10.3 The Central Limit Theorem......Page 338
10.4 Construction of Sample Spaces......Page 341
10.5 The Wiener Process......Page 343
10.6 Notes and References......Page 349
11.1 Topological Groups and Haar Measure......Page 352
11.2 Hausdorf Measure......Page 361
11.3 Self-similarity and Hausdorf Dimension......Page 368
11.4 Integration on Manifolds......Page 374
11.5 Notes and References......Page 376
Bibliography......Page 378
Index of Notation......Page 390
Index......Page 392

Many areas of mathematics utilize an imaginary variable with a real variable to form a complex number. Real analysis, as the name implies, is the section of mathematics that studies the functions of a real variable. Real variables are involved in such areas as measurements, integration, and topology. This book covers this fundamental terrain, including complete coverage of measure and integration theory, some point set topology, and rudiments of functional analysis.

Real Analysis studies the functions of a real variable, including such areas as measurements and integration and topology. Over 450 exercises of varying levels are included to give readers practice in working with the ideas presented

2011-08-31