A STRONG LAW FOR B-VALUED ARRAYS

Let (B, parallel to .parallel to) be a real separable Banach space and {X(n,k); n greater than or equal to 1, 1 less than or equal to k less than or equal to n} a triangular array of lid B-valued random variables. Set S(n) = Sigma(k=1)(n) X(n,k),n greater than or equal to 1, and Log t = log max {e, t}, t is an element of R. In this paper, we characterize the limit behavior of S(n)/root 2nLogn, n greater than or equal to 1. As an application of our result, we resolve an open problem posed by Hu and Weber (1992), The:case of row-wise independent arrays is also dealt with.