Convergence of Weighted Sums and Strong Law of Large Numbers for Convex Compact Integrable Random Sets and Fuzzy Random Sets

摘要

We prove several results in the a.s. convergence of weighted sums and strong law of large numbers for convex compact integrable random sets in separable Banach spaces via the norm compactness of the expectation of convex compact integrable random sets and an embedding method. The techniques are applied to prove strong law of large numbers for fuzzy random variables and other related results. Tightness conditions are discussed in comparison with earlier results in the literature.