Convex analysis and variational problems
Convex analysis and variational problems
Fuzzy Measure Theory
On the continuity of the concave integral
Fuzzy Sets and Systems
Time Continuity and Nonadditive Expected Utility
Mathematics of Operations Research
Information Sciences: an International Journal
A discrete Choquet integral for ordered systems
Fuzzy Sets and Systems
International Journal of Approximate Reasoning
A probabilistic representation of exact games on σ-algebras
Fuzzy Sets and Systems
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This paper investigates the concave integral for capacities defined over large spaces. We characterize when the integral with respect to capacity v can be represented as the infimum over all integrals with respect to additive measures that are greater than or equal to v. We introduce the notion of loose extendability and study its relation to the concave integral. A non-additive version for the Levi theorem and the Fatou lemma are proven. Finally, we provide several convergence theorems for capacities with large cores.