On the continuity of the concave integral
Whenever a functional is concave it is natural to ask whether its sendograph is a closed convex set. If so, the Hahn-Banach theory implies that the functional can be represented as the infimum of all continuous linear functionals greater than or equal to it. We refer to such representation as a dual representation. Dominated convergence of the concave integral for capacities is characterized in terms of dual representation whenever sequences of functions converge pointwise outside a set of zero capacity. (C) 2008 Elsevier B.V. All rights reserved.
continuity concave integral dual representation