ON THE TIGHTNESS OF CAPACITIES ASSOCIATED WITH SUB-MARKOVIAN RESOLVENTS

This paper investigates the tightness property of the capacity induced by the reduction operator with respect to the resolvent of a right Markov process. Tightness is verified in two particular situations: under the ‘weak duality hypothesis’, and if a substitute for ‘the axiom of polarity for the dual theory’ holds. In the second context, the quasi-continuity property for the excessive functions is derived. These are extensions and improvements of results of Lyons and Röckner, Ma and Röckner, Le Jan, and Fitzsimmons, mainly obtained in the context of Dirichlet forms.