Contents Preface ix Notation x Acknowledgments xv Chapter 1. Measure theory 1 §1.1. Prologue: The problem of measure 2 §1.2. Lebesgue measure 15 §1.3. The Lebesgue integral 38 §1.4. Abstract measure spaces 66 §1.5. Modes of convergence 94 §1.6. Differentiation theorems 108 §1.7. Outer measures, pre-measures, and product measures 148 Chapter 2. Related articles 173 §2.1. Problem solving strategies 174 §2.2. The Rademacher differentiation theorem 187 §2.3. Probability spaces 192 §2.4. Infinite product spaces and the Kolmogorov extension theorem 194 Bibliography 201 vii
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