Fubini-Like Theorem of Real-Valued Choquet Integrals for Set-Valued Mappings

Abstract

The purpose of this paper is to establish a Fubini-like theorem of real-valued Choquet integrals for set-valued mappings in the frame of capacity theory. To this, we introduce the comonotonic random sets and slice-comonotonic set-valued mappings, which to make good use of the comonotonic additivity of Choquet integrals.