Abstract: Let be a sequence of i.i.d. random variables and let
and be sequences of constants where Let
be a rearrangement of such that
Consider the sequence of weighted sums and, for fixed
set i.e., is the sum
minus the sum of the ’s multiplied by their corresponding coefficients
for The main results provide sufficient and, separately, necessary
conditions for almost surely for some sequence of centering
constants The current work extends that of Mori [14], [15] wherein