On the strong law of large numbers and Lp-convergence for double arrays of random elements in p-uniformly smooth Banach spaces

The aim of this paper is to establish some strong laws of large numbers and Lp-convergence for double arrays of random elements in p-uniformly smooth Banach spaces. We also provide a new characterization of p-uniformly smooth Banach spaces in terms of a strong law of large numbers for double arrays.