In this paper, we present some results concerning the concept of \(\{a_{m,n,i,j}\}\) -stochastic domination for double arrays of random variables and relationships between the concept of \(\{a_{m,n,i,j}\}\) -stochastic domination and the concept of \(\{a_{m,n,i,j}\}\) -uniform integrability, where \(\{k_m,m\ge 1\}\) and \(\{l_n,n\ge 1\}\) are two sequences of positive integers and \(\{a_{m,n,i,j};1\le i\le k_m,1\le j\le l_n,m,n\ge 1\}\) is an array of positive constants satisfying \(\begin{aligned} \sup \limits _{m\ge 1,n\ge 1}\sum \limits _{i=1}^{k_m}\sum \limits _{j=1}^{l_n}a_{m,n,i,j}=C_0, C_0\in (0,\infty ). \end{aligned}\) Applications to stochastically dominated in the Cesàro sense and on the weak law of large numbers for double arrays of random variables are obtained. The main results establish double sum versions of some results of Thành [Test, 2023].
