Limit theorems for certain functionals of unions of random closed sets

Let $X_1,X_2,\dots$ be a sequence of independent identically distributed random closed subsets of a certain locally compact, Hausdorff, and separable space $E$. For each random closed set $Y$ we consider its avoidance functional $Q_Y(F)$ equal to the probability that $Y$ is disjoint with the closed subset $F\subseteq E$. The purpose of this paper is to establish limit theorems for the random variables $Q_Y(X_1\cup\dots\cup X_n)$. The results obtained are then applied for asymptotic analysis of the mean width of convex hulls generated by uniform samples on a multidimensional ball.