A Continuity Theorem for Cores of Random Closed Sets

If a sequence of random closed sets Xn in a separable complete metric space converges in distribution in the Wijsman topology to X, then the corresponding sequence of cores (sets of probability measures dominated by the capacity functional of Xn) converges to the core of the capacity of X. Core convergence is achieved not only in the Wijsman topology, but even in the stronger Vietoris topology. This is a generalization for unbounded random sets of the result proved by Artstein for random compact sets using the Hausdorff metric.