Mesures dominées par une capacité alternée d’ordre 2

Abstract

Let C be an alternating capacity of order 2 on a metrizable compact space, and let P C {\mathcal {P}_C} be the convex set of all measures dominated by C. We find a quite simple set of extreme elements of P C {\mathcal {P}_C} such that the closed convex hull of this set is P C {\mathcal {P}_C} . We also give other properties, including a generalization of one of Anger’s results.