Negative association and negative dependence for random upper semicontinuous functions, with applications

The aim of this paper is to construct the notions of negative association and negative dependence for random upper semicontinuous functions. Besides giving some properties for these notions, we obtain inequalities which form maximal inequality and Hájek–Rényi’s type inequality. In addition, some laws of large numbers are established under various settings and they are extensions for corresponding ones in the literature.