Strong laws of large numbers for normed linear spaces

Abstract

?Strong laws of large numbers which are useful in the theory and applications of stochastic processes are obtained for sequences of independent random elements in separable normed linear spaces. The hypotheses for these results lie between those for the identically distributed case and the independent non-identieally distributed case. These results and other strong and weak laws of large numbers for separable normed linear spaces can be extended to separable Freshet spa?es. Finally, the results are applied to separable Wiener processes on [0, 1] and on [0, oo).