CHOQUET-TYPE INTEGRAL-REPRESENTATION OF POLYSUPERMEDIAN MEASURES

Some aspects of multi-parameter potential theory are developed: we giv e a Choquet-type integral representation for measures which are superm edian for a countable family of submarkovian resolvents of commuting k ernels on a Radon measurable space. For the subclass of polysupermedia n measures we prove a Riesz-type decomposition, and we show that there is a 'unique' integral representation by minimal polysupermedian meas ures. The setting covers a variety of very different examples like ran dom fields, measures on product spaces which are supermedian for resol vents on the factor spaces, and completely supermedian measures.