Stopping times and directed processes

Title ......Page 5
Copyright ......Page 6
Contents ......Page 7
Preface ......Page 11
1. Stopping times ......Page 15
1.1. Definitions ......Page 16
1.2. The amatt convergence theorem ......Page 23
1.3. Directed processes and the Radon-Nikodym theorem ......Page 27
1.4. Conditional expectations ......Page 33
2. Infinite measure and Orlicz spaces ......Page 47
2.1. Orlicz spaces ......Page 48
2.2. More on Orlicz spaces ......Page 65
2.3. Uniform integrability and conditional expectation ......Page 82
3.1. The three-function inequality ......Page 96
3.2. Sharp maximal inequality for martingale transforms ......Page 113
3.3. Prophet compared to gambler ......Page 117
4. Directed index set ......Page 127
4.1. Essential and stochastic convergence ......Page 128
4.2. The covering condition (V) ......Page 141
4.3. Lip-bounded martingales ......Page 158
4.4. Ll-bounded martingales ......Page 173
5. Banach-valued random variables ......Page 185
5.1. Vector measures and integrals ......Page 186
5.2. Martingales and amarts ......Page 197
5.3. The Radon-Nikodym property ......Page 212
5.4. Geometric properties ......Page 232
5.5. Operator ideals ......Page 246
6.1. Maximal inequalities for supermartingales ......Page 268
6.2. Decompositions of submartingales ......Page 281
6.3. The norm of the square function of a martingale ......Page 287
6.4. Lifting ......Page 294
7.1. Derivation in R ......Page 305
7.2. Derivation in Rd ......Page 314
7.3. Abstract derivation ......Page 322
7.4. D-bases ......Page 341
8. Pointwise ergodic theorems ......Page 358
8.1. Preliminaries ......Page 359
8.2. Weak maximal inequalities ......Page 364
8.3. Hopf's decomposition ......Page 369
8.4. The a-algebra of absorbing sets ......Page 370
8.5. The Chacon-Ornstein theorem (conservative case) ......Page 375
8.6. Superadditive processes ......Page 379
9. Multiparameter processes ......Page 396
9.1. A multiparameter convergence principle ......Page 397
9.2. Multiparameter Cesaro averages of operators ......Page 404
9.3. Multiparameter ratio ergodic theorems ......Page 408
9.4. Multiparameter martingales ......Page 410
References ......Page 421
Index of names ......Page 432
Index of terms ......Page 435
Cover ......Page 443