Weak Law of Large Numbers and Mean Convergence for Weighted Sums of Multidimensional Arrays Under Gut’s Condition

A new concept of weight-array-based stochastic domination in the Cesàro sense is developed. Under Gut’s condition, we establish the weak law of large numbers and Lr-convergence for weighted sums of multidimensional arrays of pairwise negatively quadrant dependent random variables. These results improve and extend corresponding known results in the literature.