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

Francesco S. de Blasi; Luca Tomassini

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arXiv · 1110.6187

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

Francesco S. de Blasi·Luca Tomassini

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Abstract

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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BibTeX RIS

Francesco S. de Blasi, Luca Tomassini. 2011-10-27. Convexification in the limit and strong law of large numbers for closed-valued random sets in Banach spaces. https://arxiv.org/abs/1110.6187

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