Strong limit theorems for negatively associated random variables with general moment conditions

Let X,Xn,n≥1 be a sequence of negatively associated random variables with identical distribution, an,n≥1 be a sequence of positive constants with an/n↑. The strong law of large numbers and complete convergence for X,Xn,n≥1 were obtained. These results are equivalent to the general moment condition ∑∞n=1P(|X|>an)<∞. On the other hand, the results extend the corresponding ones for pairwise independent random variables with identical distribution.