Law of large numbers for weak Fubini-independent random variables under capacities without sub-additivity

Abstract

This article attempts to establish the law of large numbers for random variables in Choquet expectation spaces where the Choquet integral is not sub-additive. As a basis, the Fubini-independence of random variables is generalized to a weaker version. Then the strong and weak law of large numbers are proved for weak-Fubini independent random variables under capacities which are not sub-additive.