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
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