Strong laws of large numbers for general random variables in sublinear expectation spaces

In this paper, we obtain the equivalent relations between Kolmogorov maximal inequality and Hájek–Rényi maximal inequality both in moment and capacity types in sublinear expectation spaces. Based on these, we establish several strong laws of large numbers for general random variables and obtain the growth rate of the partial sums. In a first application, a strong law of large numbers for negatively dependent random variables is obtained. In a second application, we consider the normalizing sequence {logn}n≥1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\{\log n\} _{n\ge 1}$\end{document} and get some special limit properties in sublinear expectation spaces.