On the kolmogorov–feller–gut weak law of large numbers for triangular arrays of rowwise and pairwise negatively dependent random variables

This paper proves that if the sufficient condition for the Kolmogorov–Feller–Gut weak law of large numbers is satisfied, then the corresponding sequence of partial sums converges in mean. The underlying random variables are only assumed to be pairwise negatively dependent. The proof is based on a von Bahr–Esseen-type inequality for pairwise negatively dependent random variables and some properties of regularly varying functions. The main theorems strengthen several results in the literature.