Additive representations of non-additive measures and the Choquet integral
Real-valued mappings \(v\) defined on a finite algebra are considered satisfying the condition \(v(\emptyset)= 0\) (so-called non-additive measures or capacities). Various properties of the Choquet integral with respect to \(v\) are considered. Especially, a Radon-Nikodým derivative is defined and Bayesian update of a non-additive measure is derived from an additive one. Interpretations of the results are presented and their relation to the theory of expected utility maximization is discussed.
scientific article; zbMATH DE number 698931
scientific article