Introduction. Let X= [X ny % n, n g: 1} be a martingale on a probability space (Ω, fj, P), where g^cg^c are sub-o -fields of $• Denote d n = x n —x n.. l9 x 0 ΞΞ 0, s n = (x λ + + :r n)/w for n = l, 2, . The classical martingale convergence theorem asserts that lim x n ...