Abstract
We consider capacity (fuzzy measure, non-additive probability) on a compactum
as a monotone cooperative normed game. Then it is natural to consider probability
measures as elements of core of such game.
We prove a topological version of the 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.
Publisher
Uniwersytet Mikolaja Kopernika/Nicolaus Copernicus University