Abstract
Let {Xn,nâ„1} be a sequence of random variables which is stochastically dominated by a random variable. Let {an,nâ„1} and {bn,nâ„1} be sequences of real numbers with 0<bnââ. Sufficient conditions are given under which âi=1naiXi/bnâ0 almost surely. No conditions are imposed on the joint distributions of the {Xn}. Our results generalize and improve some known results of the strong law of large numbers for random variables. We also give two examples which show the sharpness of our results.
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