FINITE AND PROFINITE CHOQUET CAPACITIES

We define the Choquet capacities in the finite case by using a non-deg enerated bilinear form associated to the Choquet base. We show that, i n the finite case, giving a Choquet capacity is equivalent to consider ing a convex set of measure. The profinite case, from the trees, is ob tained as the projective limit of the finite case. Over profinite capa cities, we define a bilinear form and study its connections with integ ration in simple cases.