Let {X,X n ,n 1} be a sequence of independent and identically distributed random variables with partial sumsif and only if EX = 0 , EX 2 = 1 and E(X 2 / log |X|) r < , where r > 1 .The paper will extend the result to the weighted sums under some conditions both on the weights and the moment.
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Liu et al. (2022) studied this question.
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