強調將學科的抽象和具體方面結合起來,用后者去解釋和啟發前者。一些主要原理(如Littlewood的三原理)提供了對學科的直覺能力,這種關鍵作用也在書中得以強調。全書通篇包含大量習題,它們發展了理論的重要方面,從而成為《測度論引論(英文版)》整體的一部分。
Preface
Notation
Acknowledgments
Chapter 1. Measure theory
1.1. Prologue: The problem of measure
1.2. Lebesgue measure
1.3. The Lebesgue integral
1.4. Abstract measure spaces
1.5. Modes of convergence
1.6. Differentiation theorems
1.7. Outer measures, pre-measures, and product measures
Chapter 2. Related articles
2.1. Problem solving strategies
2.2. The Rademacher differentiation theorem
2.3. Probability spaces
2.4. Infinite product spaces and the Kolmogorov extension theorem
Bibliography
Index