ON CONVERGENCE IN MEAN FOR DOUBLE ARRAYS OF PAIRWISE INDEPENDENT RANDOM VARIABLES

Tóm tắt

In this paper, we prove a theorem on convergence in mean of order p for double arrays of pairwise independent random variables, where 1 ≤ p < 2. We obtain Theorem 2.5 in Hong and Hwang [3] as a special case of the main result. The proof is based on the von Bahr–Essen inequality for pairwise independent random variables which is proved recently by Chen, Bai and Sung [1].