Nonlinear functionals on C(X) and Choquet integrals

摘要

We establish a retraction from monotone functionals (defined on C(X), where X is a compact Hausdorff space) with pointwise convergence topology to functionals represented by Choquet integrals with respect to monotone measures. We prove an analogue of the Riesz representation theorem in the case of Choquet integrals. (C) 2019 Elsevier B.V. All rights reserved.