Convexification in the limit and strong law of large numbers for closed-valued random sets in Banach spaces

Francesco S. de Blasi, Luca Tomassini

Published 2011-10-27Version 1

We prove a strong law of large numbers for random sets with bounded and closed values contained in an arbitrary (not necessarily separable) Banach space. We make use of a notion of convergence of sets introduced by Fisher, which is stronger than Wijsman's convergence but in general not comparable with Mosco's convergence.