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 suprepresentation 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.
All Science Journal Classification (ASJC) codes
- Countably additive measures
- Increasing convex functionals
- Regular measures
- Representation theorems