On exact capacities

Abstract

We consider capacity (fuzzy measure, non-additive probability) on a compactum as a monotone cooperative normed game. We introduce topological analogues of well known class of exact games and show that these classes form subfunctors of the capacity functor which lie between known subfunctors of convex capacities and balanced capacities. It is natural to consider probability measures as elements of core of such games. We describe exact capacities as envelopes of the convex closed sets of probability measures. Using such representation we prove openness of the functor of exact capacities. We also consider strongly exact capacities and pose the problem of coincidence of these two classes.