On the potential theory of symmetric Markov processes (Q1092520)

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.