Bulletin of the
Korean Mathematical Society BKMS

Let $\{X, X_n, n\ge 1\}$ be a sequence of i.i.d. random
variables and $\{a_{ni}, 1\le i\le n, n\ge 1 \}$ be an array of
constants. Let $\phi (x)$ be a positive increasing function on
$(0, \infty)$ satisfying $\phi(x) \uparrow \infty \quad \text{and}
\quad \phi(Cx)=O(\phi(x))$ for any $C>0.$ When $EX=0$ and $E[\phi
(|X|)]<\infty,$ some conditions on $\phi$ and $\{a_{ni}\}$ are
given under which
$\sum_{i=1}^n a_{ni} X_i \to 0$ a.s.

Keywords: strong laws of large numbers, almost sure convergence, weighted sums of i.i.d. random variables, arrays

MSC numbers: 60F15