测度论(第2版影印版)(英文版)

本书是一部为初学者提供学习测度论的入门书籍 ，综合性强，清晰易懂。本版与第1版相比，篇幅扩展 100页，并新增概率一章。本书全面介绍了测度和积分 ，重在强调学习分析和测度必需的和相关的一些话题 。前几章讲述了抽象测度和积分；后一章讲述微分知 识，包括Rd上变量的处理。每章末附有代表性的习题 ，从常规题型到扩展训练都有涉及，较高难度的习题 附有提示。

Introduction 1 Measures 1.1 Algebras and Sigma-Algebras 1.2 Measures 1.3 Outer Measures 1.4 Lebesgue Measure 1.5 Completeness and Regularity 1.6 Dynkin Classes 2 Functions and Integrals 2.1 Measurable Functions 2.2 Properties That Hold Almost Everywhere 2.3 The Integral 2.4 Limit Theorems 2.5 The Riemann Integral 2.6 Measurable Functions Again, Complex-Valued Functions, and Image Measures 3 Convergence 3.1 Modes of Convergence 3.2 Normed Spaces 3.3 Definition of LP and LP 3.4 Properties of LP and LP 3.5 Dual Spaces 4 Signed and Complex Measures 4.1 Signed and Complex Measures 4.2 Absolute Continuity 4.3 Singularity 4.4 Functions of Finite Variation 4.5 The Duals of the LP Spaces 5 Product Measures 5.1 Constructions 5.2 Fubini's Theorem 5.3 Applications 6 Differentiation 6.1 Change of Variable in Rd 6.2 Differentiation of Measures 6.3 Differentiation of Functions 7 Measures on Locally Compact Spaces 7.1 Locally Compact Spaces 7.2 The Riesz Representation Theorem 7.3 Signed and Complex Measures; Duality 7.4 Additional Properties of Regular Measures 7.5 The μ*-Measurable Sets and the Dual ofL1 7.6 Products of Locally Compact Spaces 7.7 The Daniell-Stone Integral 8 Polish Spaces and Analytic Sets 8.1 Polish Spaces 8.2 Analytic Sets 8.3 The Separation Theorem and Its Consequences 8.4 The Measurability of Analytic Sets 8.5 Cross Sections