Abstract
In the context of a transient Borel right Markov process with a fixed excessive measure ξ, we characterize the regular strongly supermedian kernels, producing smooth measures by the Revuz correspondence. In the case of the measures charging no ξ-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 ξ-polar and ρ-negligible (ρ○U being the potential part of ξ), answering to a problem of Revuz.
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