STRONG LAW OF LARGE NUMBERS AND $L^p$-CONVERGENCE FOR DOUBLE ARRAYS OF INDEPENDENT RANDOM VARIABLES

Le Van Thanh

Abstract

           For a double array of independent random variables {X_mn , m ≥ 1, n ≥ 1}, a strong law of large numbers and the L ^p-convergence are established for the double sums

m ∑ i = 1

n ∑ j = 1

Xij , m ≥ 1, n ≥ 1 .