On the weak laws of large numbers for arrays of random variables

In this paper 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 Hong and Oh [Hong, D. H., Oh, K. S., 1995. On the weak law of large numbers for arrays. Statist. Probab. Lett. 22, 55–57]. Furthermore, we obtain a WLLN for an LpLp-mixingale array without the conditions that the mixingale is uniformly integrable and the LpLp-mixingale numbers decay to zero at a special rate.