设$\{X_{ni}:1\le i\le n,n\ge 1\}$为行间NA阵列, $g(x)$是$R^{+}$上指数为$\alpha$的正则变化函数,$r>0$, $m$为正整数, $\{a_{ni}:1\le i\le n,n\ge 1\}$为满足条件$\underset{1\le i\le n}{max}|a_{ni}|=O((g(n){)}^{-1})$ 的实数阵列, 本文得到了使$\sum\limits_{n=1}^{\infty}n^{r-1}\Pr\big(\big| \sum\limits_{1\leq i_1< \cdots\epsilon\big) <\infty, \mbox{ }\forall\varepsilon>0$ 成立的条件, 推广并改进了Stout及王岳宝和苏淳等的结论.

Let $\{X_{ni}:1\le i\le n,n\ge 1\}$ be an array of rowwise NA random variables, and let $g(x)$ be a regular function with index $\alpha$. Let $\{a_{ni}:1\le i\le n,n\ge 1\}$ be an array of real numbers satisfying $\underset{1\le i\le n}{max}|a_{ni}|=O((g(n){)}^{-1})$. Let $r>0$, and let $m$ be a positive integer. A set of sufficient conditions such that $\sum\limits_{n=1}^{\infty}n^{r-1} \Pr\Big(\Big|\sum\limits_{1\leq i_1<\cdots\varepsilon\Big)<\infty, \mbox{ }\forall\varepsilon>0$ are obtained. The well-known results by Stout and Wang are extended.