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On the strong law of large numbers for weighted sums of negatively superadditive dependent random variables. (English) Zbl 1334.60039
Summary: Let $$\{X_n, n\geq 1\}$$ be a sequence of negatively superadditive dependent random variables. In this paper, we study the strong law of large numbers for general weighted sums $$\frac{1}{g(n)}\sum_{i=1}^n\frac{X_i}{h(i)}$$ of negatively superadditive dependent random variables with non-identical distribution. Some sufficient conditions for the strong law of large numbers are provided. As applications, the Kolmogorov strong law of large numbers and the Marcinkiewicz-Zygmund strong law of large numbers for negatively superadditive dependent random variables are obtained. Our results generalize the corresponding ones for independent random variables and negatively associated random variables.

##### MSC:
 60F15 Strong limit theorems
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