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It is pointed out that a general theorem presented in Yu Miao and Shoufang Xu’s paper has a serious gap. In this small note, a counterexample for this theorem is provided exhibiting a triangular array of real numbers and a sequence of independent identically distributed random variables for which its conclusion fails. An reformulation of Yu Miao and Shoufang Xu’s general theorem is performed making this statement true. 2010 Mathematics Subject Classification: 60F15

Remarks on Yu Miao and Shoufang Xu's paper"Almost sure convergence of weighted sums"