The Choquet integral representability of comonotonically additive functionals in locally compact spaces Original Research Article

We give an alternative and direct approach to the Choquet integral representability of a comonotonically additive, bounded, monotone functional I defined on the space of all continuous, real-valued functions on a locally compact space X with compact support and on the space of all continuous, real-valued functions on X vanishing at infinity. To this end, we introduce the notion of the asymptotic translatability of the functional I and show that this simple notion is equivalent to the Choquet integral representability of I with respect to a monotone measure on X with appropriate regularity.