Abstract
Let be random variables and a triangular array of constants. In this paper we find the various conditions on {ani } and {Xn } under which converges to zero almost surely. It is shown that for the identically distributed random variables the conditions a.s. A generalization of Marcinkiewicz's law of large numbers is given. It is shown that for the i.i.d. case the conditions and EX = 0 imply that a.s
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