A continuity theorem for cores of random closed sets

Abstract

If a sequence of random closed sets X n 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 X n ) 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.