Journal of Convex Analysis 18 (2011), No. 1, 285--300
Copyright Heldermann Verlag 2011
On the Strong Law of Large Numbers in Spaces of Compact Sets
Francesco S. de Blasi
Dip. di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica 1, 00133 Roma, Italy
deblasi@mat.uniroma2.it
Luca Tomassini
Dip. di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica 1, 00133 Roma, Italy
tomassin@mat.uniroma2.it
[Abstract-pdf]
\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.
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