Stopping Times and Directed Processes Book

	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