Note on complete convergence and complete moment convergence for negatively dependent random variables under sub-linear expectations

In this article, we study the complete convergence and the complete moment convergence for negatively dependent (ND) random variables under sub-linear expectations. Under proper conditions of the moment of random variables, we establish the complete convergence and the complete moment convergence. As applications, we obtain the Marcinkiewcz-Zygmund type strong law of large numbers of ND random variables under sub-linear expectations. The results here generalize the corresponding ones in classic probability space to those under sub-linear expectations.