More on complete convergence for arrays

A complete convergence theorem for arrays of rowwise independent random variables was proposed by Hu et al. (Statist. Probab. Lett. 38 (1998) 27). Two years later, Hu and Volodin (Statist. Probab. Lett. 47 (2000) 209) imposed one additional condition in addendum to the paper. In this paper, we prove the complete convergence theorem without the additional condition.