English

On balanced capacities

General Topology 2021-05-25 v1 Probability

Abstract

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.

Cite

@article{arxiv.2105.11138,
  title  = {On balanced capacities},
  author = {Taras Radul},
  journal= {arXiv preprint arXiv:2105.11138},
  year   = {2021}
}
R2 v1 2026-06-24T02:23:51.896Z