内容简介
本书是Folland教授的名著《实分析》的第二版。与第一版相比，在一些内容的编排上作了适当调整，同时引入了一些新的内容，去掉了已经过时的内容，更有利于学生学习与思考。作为一部优秀的教材，内容不仅涵盖了分析学的基本内容和技巧，还介绍了一些从事其他领域的研究工作所必需的基础知识。此外，教材中的大量习题，能够进一步拓展思维，从而易于更加深入地了解这些内容背后的真实想法。本书适用于理工类专业及相关专业的研究生。
作者简介
Gerald B. Folland，1953年于美国普林斯顿大学获得数学博士学位，美国华盛顿大学西雅图分校数学系教授。早年师从分析大师E.M.Stein学习，在调和分析、复分析、微分方程等领域都有着杰出的工作。他的著作《相空间中的分析》、《抽象调和分析》、《实分析》等一直是国内外数学专业以及相关专业研究生的重要参考书籍。
章节目录
Preface
0Prologue
0.1The Language of Set Theory
0.2Orderings
0.3Cardinality
0.4More about Well Ordered Sets
0.5The Extended Real Number System
0.6Metric Spaces
0.7Notes and References
1Measures
1.1Introduction
1.2a-algebras
1.3Measures
1.4Outer Measures
1.5Borel Measures on the Real Line
1.6Notes and References
2Integration
2.1Measurable Functions
2.2Integration of Nonnegative Functions
2.3Integration of Complex Functions
2.4Modes of Convergence
2.5Product Measures
2.6The n-dimensional Lebesgue Integral
2.7Integration in Polar Coordinates
2.8Notes and References
3Signed Measures and Differentiation
3.1Signed Measures
3.2The Lebesgue-Radon-Nikodym Theorem
3.3Complex Measures
3.4Differentiation on Euclidean Space
3.5Functions of Bounded Variation
3.6Notes and References
4Point Set Topology
4.1Topological Spaces
4.2Continuous Maps
4.3Nets
4.4Compact Spaces
4.5Locally Compact Hausdorff Spaces
4.6Two Compactness Theorems
4.7The Stone-Weierstrass Theorem
4.8Embeddings in Cubes
4.9Notes and References
5Elements of Functional Analysis
5.1Normed Vector Spaces
5.2Linear Functionals
5.3The Baire Category Theorem and its Consequences
5.4Topological Vector Spaces
5.5Hilbert Spaces
5.6Notes and References
6LP Spaces
6.1Basic Theory of LP Spaces
6.2The Dual of LP
6.3Some Useful Inequalities
6.4Distribution Functions and Weak LP
6.5Interpolation of LP Spaces
6.6Notes and References
7Radon Measures
7.1Positive Linear Functionats on Cc(X)
7.2Regularity and Approximation Theorems
7.3The Dual of Co(X)
7.4Products of Radon Measures
7.5Notes and References
8EIements of Fourier Analysis
8.1Preliminaries
8.2Convolutions
8.3The Fourier Transform
8.4Summation of Fourier Integrals and Series
8.5Pointwise Convergence of Fourier Series
8.6Fourier Analysis of Measures
8. 7Applications to Partial Differential Equations
8.8Notes and References
9Elements of Distribution Theory
9.1Distributions
9.2Compactly Supported, Tempered, and Periodic
Distributions
9.3Sobolev Spaces
9.4Notes and References
10Topics in Probability Theory
10.1Basic Concepts
10.2The Law of Large Numbers
10.3The Central Limit Theorem
10.4Construction of Sample Spaces
10.5The Wiener Process
10.6Notes and References
11More Measures and Integrals
11.1Topological Groups and Haar Measure
11.2Hausdorff Measure
11.3Self-similarity and Hausdorff Dimension
11.4Integration on Manifolds
11.5Notes and References
Bibliography
Index of Notation
Index
实分析（第2版）是2019年由世界图书出版公司出版,作者[美]G.B.弗兰德。
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