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On the weak laws of large numbers for arrays of random variables. (English) Zbl 1179.60012
Summary: We obtain weak laws of large numbers (WLLNs) for arrays of random variables under the uniform Cesàro-type condition. As corollary, we obtain the result of D. H. Hong and K. S. Oh [Statist. Probab. Lett. 22, 55–57 (1995; Zbl 0815.60023)]. Furthermore, we obtain a WLLN for an \(L_p\)-mixingale array without the conditions that the mixingale is uniformly integrable and the \(L_p\)-mixingale numbers decay to zero at a special rate.

MSC:
60F05 Central limit and other weak theorems
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