Representation of increasing convex functionals with countably additive measures
Volume 260 / 2021
Studia Mathematica 260 (2021), 121-140 MSC: Primary 47H07, 28C05, 28C15. DOI: 10.4064/sm181107-16-2 Published online: 1 April 2021
We derive two types of representation results for increasing convex functionals in terms of countably additive measures. The first is a max-representation of functionals defined on spaces of real-valued continuous functions and the second a sup-representation of functionals defined on spaces of real-valued Borel measurable functions. Our assumptions consist of sequential semicontinuity conditions which are easy to verify in different applications.