Convergence in -mean of weighted sums of NQD random variables

Under some conditions of uniform integrability, the L r convergence for weighted sums of arrays of rowwise linearly negative quadrant dependent random variables has been established by Wu and Guan [Y. Wu, M. Guan, Mean convergence theorems and weak laws of large numbers for weighted sums of dependent random variables, J. Math. Anal. Appl. 377 (2011) 613–623]. In this paper, we point out a gap in the proof and extend the result to rowwise pairwise negative quadrant dependent (NQD) random variables under weaker uniformly integrable conditions.