Convergence in rr-mean of weighted sums of NQD random variables

Under some conditions of uniform integrability, the LrLr 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.