Contents

Preface ix

A remark on notation x

Acknowledgments xi

Chapter 1. Real analysis

§1.1. A quick review of measure and integration theory 3

§1.2. Signed measures and the Radon-Nikodym-Lebesgue

theorem 15

§1.3.

Lp

spaces 27

§1.4. Hilbert spaces 45

§1.5. Duality and the Hahn-Banach theorem 59

§1.6. A quick review of point-set topology 71

§1.7. The Baire category theorem and its Banach space

consequences 85

§1.8. Compactness in topological spaces 101

§1.9. The strong and weak topologies 117

§1.10. Continuous functions on locally compact Hausdorff

spaces 133

§1.11. Interpolation of

Lp

spaces 157

vii