ON THE ALMOST SURE CONVERGENCE OF TWO-PARAMETER MARTINGLES AND THE STRONG LAW OF LARGE NUMBERS IN BANACH SPACES
NGUYEN VAN HUNG, NGUYEN DUY TIEN
Abstract
Let be a probability space, denote the set of parameters with the partial order defined by if and only if and . Let be an increasing family of sub--fields of satisfying the usual condition and a two-parameter martingale taking values in a Banach space . In this paper we investigate the interrelation between geometric properties of Banach spaces and Martingale convergence theorems. Moreover we also study Marcinkiewicz-Zygmund's type strong law of large numbers for two-parameter Banach-valued martingales and the integrability of two-parameter Banach-valued martingale maximal functions.