Capacities, Set-Valued Random Variables and Laws of Large Numbers for Capacities

In this paper, we shall survey some connections between the theory of set-valued random variables and Choquet theory. We shall focus on investigating some results of the relationships between the distributions of set-valued random variables and capacities, and also some connections between the Aumann integral and the Choquet integral. Then we shall review some results on laws of large numbers (LLN’s) for set-valued random variables and for capacities, and point out some relations between these two kinds of LLN’s. Finally we shall give a new strong LLN of exchangeable random variables for capacities.

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