On infinite perfect graphs and randomized stopping points on the plane (Q1093246)

We show that perfection of polytopes defined by infinite zero-one matrices can be characterized as in the finite case through an appropriate definition of infinite perfect graphs. We examine the relationship between certain such polytopes and a convex set of random measures on the discrete plane, termed randomized stopping points, that appear in the context of the optimal stopping problem for two-parameter processes. Using probabilistic techniques, we show that under a conditional qualitative independence hypothesis on the underlying filtration, which we express as a commutation property of a ``conditional supremum'' operator, the only extremal elements of this set of random measures are ordinary stopping points.