A fine domination principle for excessive measures
type: Item
instance of: scholarly article
title: A fine domination principle for excessive measures
zbMATH Open document ID: 0713.60078
DOI: 10.1007/BF02571381
published in: Mathematische Zeitschrift
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174262
review text: 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 \textit{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.
Mathematics Subject Classification ID: 60J45
Mathematics Subject Classification ID: 31D05
zbMATH DE Number: 4174064
zbMATH Keywords: domination principle
zbMATH Keywords: excessive measures
zbMATH Keywords: Radon-Nikodým derivative
zbMATH Keywords: density
zbMATH Keywords: potential
zbMATH Keywords: domination principle of K. Janssen
zbMATH Keywords: Kuznetsov measures
zbMATH Keywords: essential limits
zbMATH Keywords: potential theory
author: Patrick J. Fitzsimmons
author: R. K. Getoor
MaRDI profile type: Publication
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OpenAlex ID: W1988020516
description: scientific article; zbMATH DE number 4174064