ON THE CENTRAL LIMIT THEOREM WITH ALMOST SURECONVERGENCE

Peter Schatte

Abstract: Let be the partial sums of i.i.d.r.v.’s with zero means and variance one and let
be a real function. In this paper, sufficient conditions are given under which
converges almost surely to Two variants of convergence
are considered: limitation of by logarithmic means and limitation of
by arithmetic means, where Under the same
assumptions in the same sense, converges almost surely to