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In this paper, the Hájek-Rènyi inequality and the strong law of large numbers for asymptotically negatively associated random variables are obtained. In particular, the classical Marcinkiewicz strong law of large numbers for negatively associated random variables is generalized to the case of asymptotically negative association. MSC: 60F05, 60F15.

The Hájek-Rènyi inequality and strong law of large numbers for ANA random variables