On the continuity of the concave integral

Authors:
Roee Teper
Affiliations:
School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Venue:
Fuzzy Sets and Systems
Year:
2009

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Abstract

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.