Convergence properties of partial sums for arrays of rowwise negatively orthant dependent random variables

Let {Xnk, 1 ≤ k ≤ n, n ≥ 1} bean array of rowwise negatively orthant dependent random variables and let {an, n ≥ 1} be a sequence of positive real numbers with an ↑ ∞. The convergence properties of partial sums \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac1a_n\sum\nolimits_k = 1^n X_nk $$\end{document} are investigated and some new results are obtained. The results extend and improve the corresponding theorems of rowwise independent random variable arrays by Hu and Taylor [Hu, T. C., Taylor R. L. (1997). On the strong law for arrays and for the bootstrap mean and variance. International Journal of Mathematics and Mathematical Sciences, 20(2), 375–382].