Extreme Points of Certain Sets of Probability Measures, with Applications

Let K be the set of probability measures on a metric space having prescribed values for the integrals of (a finite number of) prescribed functions f_i. Extreme points of K are characterized in general. Under a restriction on the f_i extreme points and more general faces of K are characterized. Applications to inverse balayage problems, measures with prescribed moments or values of Laplace transforms, measures with prescribed marginal distributions and the queueing system GI/M/1 are presented.