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For weighted sums, general strong laws of large numbers of the form almost certainly are established where the random variables are stochastically dominated by a random variable are suitable conditional expectations or are all 0. The hypotheses involve both the behavior of the tail of the distribution of ∣Y∣ and the growth behavior of the constants bn/an. In general, no assumptions are made regarding the joint distributions of . As special cases, both old and new results are obtained
Adler et al. (Thu,) studied this question.