A NEGATIVE VERSION OF CHOQUET THEOREM FOR POLISH SPACES

Hung T. Nguyen, Nguyen To Nhu

Abstract


The foundations of random closed sets onlocal ly compact separable Haus-dorff spacesare essentially based upon the Choquet theorem characterizing distributions of random sets as capacities alternating of innite order dened on compact sets or on open sets Since the natural domain of probabilityis Polish spaces it is necessary to know whether or not Choquet theorem holds in non locally compact spaces In this note weprovide an example showing that in a
sense the answer is negative.

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