On the Strong Law of Large Numbers in Spaces of Compact Sets

F. S. de Blasi ; L. Tomassini

Journal of convex analysis, Tome 18 (2011) no. 1, pp. 285-3

Résumé

\def\bE{{\mathbb E}} \def\bR{{\mathbb R}} \def\cK{{\cal K}} \def\fY{{\mathfrak Y}} Let $\fY$ be the space of all nonempty compact subsets of $\bR^d$ and let $\cK(\fY)$ be the space of all nonempty compact subsets of $\fY$. For a random set with values in $\cK(\fY)$, after defining the expectation, we establish a version of the strong law of large numbers. Some related results concerning the case of nonempty compact convex subsets of a Banach space $\bE$ are included.