p-adic Choquet Theory

A non-archimedean version of the classical Choquet Theory is developped. Thus, the connection between a probability measure mu on a compact subset X of a locally convex space (over a non-archimedean valued field) and its barycenter z(mu) is established. Special attention is given to the case where X is a simplex i.e. when mu -> z(mu) is a horneomorphisnt. Examples illustrating the theory are presented.