Complete Convergence and Strong Laws of Large Numbers for Double Arrays of Convex Compact Integrable Random Sets and Applications for Random Fuzzy Variables

We prove some fairly general results of the complete convergence for maximum partial double sums and strong law of large numbers for double arrays of real and Banach valued random variables. Then using the norm compactness of the expectation of convex compact integrable random sets and an embedding method, we improve several results for maximum partial double sums of convex compact integrable random sets under some new conditions on the support functions. We also provide a typical example illustrating this study. Further applications to the strong law of large numbers for random fuzzy convex upper semicontinuous variables are given.