An improved version of a result of Chandra, Li, and Rosalsky

For an array of rowwise pairwise negative quadrant dependent, mean 0 random variables, Chandra, Li, and Rosalsky provided conditions under which weighted averages converge in \(\mathscr{L}_{1}\) to 0. The Chandra, Li, and Rosalsky result is extended to \(\mathscr{L}_{r}\) convergence (\(1\leq r<2\)) and is shown to hold under weaker conditions by applying a mean convergence result of Sung and an inequality of Adler, Rosalsky, and Taylor.