On strong laws of large numbers for arrays of rowwise independent random elements - Abolghassem Bozorgnia; Ronald Frank Patterson; Robert Lee Taylor (International Journal of Mathematics and Mathematical Sciences)
Let Xnk be an array of rowwise independent random elements in a separable Banach space of type r, 1≤r≤2. Complete convergence of n1/p∑k=1nXnk to 0, 0<p<r≤2 is obtained when sup1≤k≤nE ‖Xnk‖v=O(nα), α≥0 with v(1p−1r)>α+1. An application to density estimation is also given.