Smooth measures and regular strongly supermedian kernels generating sub-Markovian resolvents

摘要

In the context of a transient Borel right Markov process with a fixed excessive measure xi, we characterize the regular strongly supermedian kernels, producing smooth measures by the Revuz correspondence. In the case of the measures charging no xi -semipolar sets, this is the analytical counterpart of a probabilistic result of Revuz, Fukushima, and Getoor and Fitzsimmons, concerning the positive continuous additive functionals. We also consider the case of the measures charging no set that is both xi -polar and rho -negligible (rho circle U being the potential part of xi), answering to a problem of Revuz. [References: 19]