ABSTRACT
Let {Xnk, k ⩾ 1, n ⩾ 1} be an array of rowwise ANA random variables stochastically dominated by a random variable X, and {ank, 1 ⩽ k ⩽ n, n ⩾ 1} be an array of real numbers with for some 0 ⩽ α ⩽ 2. Under the almost optimal moment conditions, the paper shows that
In addition, we can get the strong law of large numbers for sequence of ANA random variables as application of our Theorem.