Bulletin of the
Korean Mathematical Society BKMS

Let $\{X_{nk},\ u_n\le k\le v_n,\ n\ge 1\}$ be an array of rowwise independent,
but not necessarily identically distributed, random variables with $EX_{nk}=0$ for all $k$ and $n.$
In this paper, we povide a domination condition under which $\sum_{k=u_n}^{v_n}X_{nk}/n^{1/p}$,
$1\le p<2,$ converges completely to zero.

Keywords: complete convergence, arrays, rowwise independent random variables, moving average

MSC numbers: 60F15