Abstract

Let Y\fY be the space of all nonempty compact subsets of Rd\bR^d and let K(Y)\cK(\fY) be the space of all nonempty compact subsets of Y\fY. For a random set with values in K(Y)\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 E\bE are included

Author information

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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

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Suggested citation

F. S. de Blasi, L. Tomassini. “On the Strong Law of Large Numbers in Spaces of Compact Sets.” Journal of Convex Analysis 18 (2011), No. 1, 285–300. https://doi.org/10.68381/jca18016

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Published by Heldermann Verlag, 2011. Rights now held by Banach Press LLC.