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Preface | ||
1 | Stopping times | 1 |
1.1 | Definitions | 2 |
1.2 | The amart convergence theorem | 9 |
1.3 | Directed processes and the Radon-Nikodym theorem | 13 |
1.4 | Conditional expectations | 19 |
2 | Infinite measure and Orlicz spaces | 33 |
2.1 | Orlicz spaces | 34 |
2.2 | More on Orlicz spaces | 51 |
2.3 | Uniform integrability and conditional expectation | 68 |
3 | Inequalities | 82 |
3.1 | The three-function inequality | 82 |
3.2 | Sharp maximal inequality for martingale transforms | 99 |
3.3 | Prophet compared to gambler | 103 |
4 | Directed index set | 113 |
4.1 | Essential and stochastic convergence | 114 |
4.2 | The covering condition (V) | 127 |
4.3 | L[suscript psi]-bounded martingales | 144 |
4.4 | L[subscript 1]-bounded martingales | 159 |
5 | Banach-valued random variables | 171 |
5.1 | Vector measures and integrals | 172 |
5.2 | Martingales and amarts | 183 |
5.3 | The Radon-Nikodym property | 198 |
5.4 | Geometric properties | 218 |
5.5 | Operator ideals | 232 |
6 | Martingales | 254 |
6.1 | Maximal inequalities for supermartingales | 254 |
6.2 | Decompositions of submartingales | 267 |
6.3 | The norm of the square function of a martingale | 273 |
6.4 | Lifting | 280 |
7 | Derivation | 291 |
7.1 | Derivation in [actual symbols not reproducible] | 291 |
7.2 | Derivation in [actual symbols not reproducible] | 300 |
7.3 | Abstract derivation | 308 |
7.4 | D-bases | 327 |
8 | Pointwise ergodic theorems | 344 |
8.1 | Preliminaries | 345 |
8.2 | Weak maximal inequalities | 350 |
8.3 | Hopf's decomposition | 355 |
8.4 | The [sigma]-algebra of absorbing sets | 356 |
8.5 | The Chacon-Ornstein theorem (conservative case) | 361 |
8.6 | Superadditive processes | 365 |
9 | Multiparameter processes | 382 |
9.1 | A multiparameter convergence principle | 383 |
9.2 | Multiparameter Cesaro averages of operators | 390 |
9.3 | Multiparameter ratio ergodic theorems | 394 |
9.4 | Multiparameter martingales | 396 |
References | 407 | |
Index of names | 418 | |
Index of terms | 421 |
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