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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。作为一部很好的教材，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。

Preface 0 Prologue 0.1 The Language of Set Theory 0.2 Orderings 0.3 Cardinality 0.4 More about Well Ordered Sets 0.5 The Extended Real Number System 0.6 Metric Spaces 0.7 Notes and References 1 Measures 1.1 Introduction 1.2 a-algebras 1.3 Measures 1.4 Outer Measures 1.5 Borel Measures on the Real Line 1.6 Notes and References 2 Integration 2.1 Measurable Functions 2.2 Integration of Nonnegative Functions 2.3 Integration of Complex Functions 2.4 Modes of Convergence 2.5 Product Measures 2.6 The n-dimensional Lebesgue Integral 2.7 Integration in Polar Coordinates 2.8 Notes and References 3 Signed Measures and Differentiation 3.1 Signed Measures 3.2 The Lebesgue-Radon-Nikodym Theorem 3.3 Complex Measures 3.4 Differentiation on Euclidean Space 3.5 Functions of Bounded Variation 3.6 Notes and References 4 Point Set Topology 4.1 Topological Spaces 4.2 Continuous Maps 4.3 Nets 4.4 Compact Spaces 4.5 Locally Compact Hausdorff Spaces 4.6 Two Compactness Theorems 4.7 The Stone-Weierstrass Theorem 4.8 Embeddings in Cubes 4.9 Notes and References 5 Elements of Functional Analysis 5.1 Normed Vector Spaces 5.2 Linear Functionals 5.3 The Baire Category Theorem and its Consequences 5.4 Topological Vector Spaces 5.5 Hilbert Spaces 5.6 Notes and References 6 LP Spaces 6.1 Basic Theory of LP Spaces 6.2 The Dual of LP 6.3 Some Useful Inequalities 6.4 Distribution Functions and Weak LP 6.5 Interpolation of LP Spaces 6.6 Notes and References 7 Radon Measures 7.1 Positive Linear Functionats on Cc(X) 7.2 Regularity and Approximation Theorems 7.3 The Dual of Co(X) 7.4 Products of Radon Measures 7.5 Notes and References 8 EIements of Fourier Analysis 8.1 Preliminaries 8.2 Convolutions 8.3 The Fourier Transform 8.4 Summation of Fourier Integrals and Series 8.5 Pointwise Convergence of Fourier Series 8.6 Fourier Analysis of Measures 8. 7 Applications to Partial Differential Equations 8.8 Notes and References 9 Elements of Distribution Theory 9.1 Distributions 9.2 Compactly Supported, Tempered, and Periodic Distributions 9.3 Sobolev Spaces 9.4 Notes and References 10 Topics in Probability Theory 10.1 Basic Concepts 10.2 The Law of Large Numbers 10.3 The Central Limit Theorem 10.4 Construction of Sample Spaces 10.5 The Wiener Process 10.6 Notes and References 11 More Measures and Integrals 11.1 Topological Groups and Haar Measure 11.2 Hausdorff Measure 11.3 Self-similarity and Hausdorff Dimension 11.4 Integration on Manifolds 11.5 Notes and References Bibliography Index of Notation Index

Gerald B. Folland，1953年于美国普林斯顿大学获得数学博士学位，现任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。

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