A NEGATIVE VERSION OF CHOQUET THEOREM FOR POLISH SPACES

Abstract

The foundations of random closed sets on locally compact separable Haus dor spaces are essentially based upon the Choquet theorem characterizing dis tributions of random sets as capacities alternating of innite order dened on compact sets or on open sets Since the natural domain of probability is Polish spaces it is necessary to know whether or not Choquet theorem holds in non locally compact spaces In this note we provide an example showing that in a sense the answer is negative