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

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

2011-10-27

arxiv.org/abs/1110.6187v1

Mathematics

Probability

Scientific paper

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.

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