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

Let

be the space of all nonempty compact subsets of

{\mathbb R}^d R d

and let

{\cal K}({\mathfrak Y}) K ( Y )

be the space of all nonempty compact subsets of

{\mathfrak Y} Y

. For a random set with values in

{\cal K}({\mathfrak Y}) K ( Y )

, 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

{\mathbb E} E

are included