Quasi-Regular Topologies for L^p-Resolvents and Semi-Dirichlet Forms

Abstract

We prove that for any semi-Dirichlet form $(\epsilon ,D(\epsilon ))$ on a measurable Lusin space $E$ there exists a Lusin topology with the given $\sigma$-algebra as the Borel $\sigma$-algebra so that $(\epsilon ,D(\epsilon ))$ becomes quasi-regular. However one has to enlarge $E$ by a zero set. More generally a corresponding result for arbitrary $L^p$-resolvents is proven.

arXiv comment14 pages, to appear in Potential Analysis