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A fine domination principle for excessive measures. (English) Zbl 0713.60078

We present a version of the domination principle for the excessive measures of a general right process. The key point is that if we fix an excessive measure m, then any excessive measure absolutely continuous with respect to m admits a Radon-Nikodým derivative that is finely continuous off a suitable exceptional set. The domination principle is the statement that if the density of the potential of a measure \(\mu\) is dominated by the density of a second excessive measure \(\eta\), almost everywhere with respect to \(\mu\), then the potential of \(\mu\) is everywhere dominated by \(\eta\). This result sharpens earlier work of G. Mokobodzki and the first named author, and it is related to the co- fine domination principle of K. Janssen. The principal tools used are the theory of Kuznetsov measures, and the “essential limits” pioneered by Chung and Walsh. Several applications of the domination principle are made. In particular we characterize the class of m-quasi-bounded potentials, extending work of Arsove and Leutwiler in Newtonian potential theory.

MSC:

60J45 Probabilistic potential theory
31D05 Axiomatic potential theory
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