Viii CONTENTS
6. Notes and remarks 115
V. Martingales 121
1. Conditional expectations and martingales 121
2. Convergence theorems 125
3. Dentable sets and the Radon-Nikodym property 131
4. The Radon-Nikodym property for Lp(ju, X) 140
5. Notes and remarks 141
VI. Operators on spaces of continuous functions 147
1. Operators on B{2) and LJfi) 148
2. Weakly compact operators on C(Q) and the Riesz
Representation Theorem 151
3. Absolutely summing operators on C(Q) 161
4. Nuclear operators on C(0) 169
5. Notes and remarks 176
VII. Geometric aspects of the Radon-Nikodym property 187
1. The Krein-Mil'man theorem and the Radon-Nikodym
property 187
2. Separable dual spaces, the Krein-Mil'man property and
the Radon-Nikodym property 191
3. Strongly exposed points and the Radon-Nikodym
property 199
4. The Radon-Nikodym property and the existence of extreme
points for nonconvex closed bounded sets 203
5. Notes and remarks 208
6. Summary of equivalent formulations of the Radon-
Nikodym property 217
7. The Radon-Nikodym property for specific spaces 218
VIII. Tensor products of Banach spaces 221
1. The least and greatest crossnorms 221
2. The duals of Xand Y 229
3. The approximation and metric approximation properties 238
4. Applications of tensor products and vector measures to
Banach space theory 245
5. Notes and remarks 253
IX. The range of a vector measure 261
1. The Liapounoff Convexity Theorem 261
2. Rybakov's theorem 267
3. Extreme point phenomena 269
4. Notes and remarks 272
Bibliography 277
Subject index 311
Author index 319
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