  We consider capacity (fuzzy measure, non-additive probability) on a compactum
as a monotone cooperative normed game. Then it is naturally to consider
probability measures as elements of core of such game. We prove an analogue of
Bondareva-Shapley theorem that non-emptiness of the core is equivalent to
balancedness of the capacity. We investigate categorical properties of balanced
capacities and give characterizations of some fuzzy integrals of balanced
capacities.
