Complete convergence for sums of arrays of random elements - Soo Hak Sung (International Journal of Mathematics and Mathematical Sciences)
Let Xni be an array of rowwise independent B-valued random elements and {an} constants such that 0<an↑∞. Under some moment conditions for the array, it is shown that ∑i=1nXni/an converges to 0 completely if and only if ∑i=1nXni/an converges to 0 in probability.