Characteristic function for random sets and convergence of sums of independent random sets (Q1577614)

The author introduces the notion of characteristic function for random sets with values in closed bounded convex subsets of a Banach space with separable topological dual. The main interest of this characteristic function is that it connects distributions of random sets with distributions of random vectors. The classical results on the convergence of independent random variables are extended to the case of independent random sets with closed and bounded convex values.