This paper deals with a generalization of the classical Choquet theorem. We consider metric spaces which are endowed with an abstract notion of convexity. Convex combinations are obtained by the solutions of variational inequalities. A generalized Krein-Milman theorem is derived from our Choquet theorem. We end with an example based on hyperbolic geometry.
Cite this article
T. Okon, Choquet Theory in Metric Spaces. Z. Anal. Anwend. 19 (2000), no. 2, pp. 303–314DOI 10.4171/ZAA/952