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On the potential theory of symmetric Markov processes. (English) Zbl 0627.60067

Let X be a Borel right process that is symmetric relative to a \(\sigma\)- finite measure m. It is shown that if \(\mu\) is a finite measure on the state space of X, then \(\mu P_ t\ll m\) for all \(t>0\) if and only if \(\mu\) charges no finely open m-polar set; this in turn is equivalent to \(\mu U^ q\ll m\) for one, and hence all \(q\geq 0.\)
It is further shown that every excessive function of finite energy is the potential of a measure. In particular every Borel set of finite capacity has a capacitary measure. The methods are “elementary” in that no deep results from the theory of Dirichlet spaces or the theory of additive functionals are required.

MSC:

60J45 Probabilistic potential theory
60J55 Local time and additive functionals
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