L. Beznea et N. Boboc, Smooth measures and regular strongly supermedian kernels generating sub-Markovian resolvents, POTENT ANAL, 15(1-2), 2001, pp. 77-87
In the context of a transient Borel right Markov process with a fixed exces
sive measure xi, we characterize the regular strongly supermedian kernels,
producing smooth measures by the Revuz correspondence. In the case of the m
easures 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 t
he case of the measures charging no set that is both xi -polar and rho -neg
ligible (rho circle U being the potential part of xi), answering to a probl
em of Revuz.