导语

  

内容提要

  

    D.W.斯特鲁克著的《简明积分导论（第3版影印版）（英文版）》是一部关注度很高的教科书，内容独特、简明，逻辑性强，自成一体，为有志成为全职分析师、物理学家、工程师和经济师的读者，介绍了测度论基础知识。与上一版相比，第3版新增傅里叶变换一章。本书的另一个突出特点是书后附有全部习题解答。本书也可作为相关专业的读者自学读本。

Preface to Third Edition
Preface to Second Edition
Preface to First Edition
Chapter I The Classical Theory
  1.1 Riemann Integration
  1.2 Riemann-Stieltjes Integration
Chapter II Lebesgue Measure
  2.0 The Idea
  2.1 Existence
  2.2 Euclidean Invariance
Chapter III Lebesgue Integration
  3.1 Measure Spaces
  3.2 Construction of Integrals
  3.3 Convergence of Integrals
  3.4 Lebesgue's Differentiation Theorem
Chapter IV Products of Measures
  4.1 Fubini's Theorem
  4.2 Steiner Symmetrization and the Isodiametric Inequality
Chapter V Changes of Variable
  5.0 Introduction
  5.1 Lebesgue vs. Riemann Integrals
  5.2 Polar Coordinates
  5.3 Jacobi's Transformation and Surface Measure
  5.4 The Divergence Theorem
Chapter VI Some Basic Inequalities
  6.1 Jensen, Minkowski, and Holder
  6.2 The Lebesgue Spaces
  6.3 Convolution and Approximate Identities
Chapter VII Elements of Fourier Analysis
  7.1 Hiobert Space
  7.2 Fourier Series
  7.3 The Fourier Transform, L1-theory
  7.4 Hermite Functions
  7.5 The Fourier Transform, L2-theory
Chapter VIII A Little Abstract Theory
  8.1 An Existence Theorem
  8.2 The Radon-Nikodym Theorem
Solution Manual
Notation
Index