On the Mean Convergence for Double Arrays of Dependent Random Variables

In this paper, we prove a weak law of large numbers and a mean convergence theorem for double arrays of random variables satisfying Condition \((G_{2})\) , where \(1\leq p<2\) . The main results establish a double sum version of Theorems 2.1 and 2.2 of Thành [Statistical Papers, 2023, https://doi.org/10.1007/s00362-023-01427-y].