Strong Laws for Martingale Differences and Independent Random Variables

A strong law of large numbers (SLLN) for martingale differences {X _n,_n,n1} permitting constant, random or hybrid normalizations, is obtained via a related SLLN for their conditional variances E{X _n ² |_n-1}n1. This, in turn, leads to martingale generalizations of known results for sums of independent random variables. Moreover, in the independent case, simple conditions are given for a generalized SLLN which contains the classical result of Kolmogorov when the variables are i.i.d.