A continuity theorem for cores of random closed sets

Terán, Pedro

doi:10.1090/S0002-9939-08-09412-4

A continuity theorem for cores of random closed sets
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by Pedro Terán PDF

Proc. Amer. Math. Soc. 136 (2008), 4417-4425

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.

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