ON COMPLETE CONVERGENCE FOR ARRAYS OF ROWWISE INDEPENDENT RANDOM ELEMENTS Sung Soo-Hak; Cabrera Manuel Ordonez; Hu Tien-Chung;
A complete convergence theorem for arrays of rowwise independent random variables was proved by Sung, Volodin, and Hu . In this paper, we extend this theorem to the Banach space without any geometric assumptions on the underlying Banach space. Our theorem also improves some known results from the literature.
Banach space valued random elements;complete convergence;rowwise independence;sums of independent random elements;convergence in probability;