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

Abstract

We prove that for any semi-Dirichlet form $(ε, D(ε))$ on a measurable Lusin space $E$ there exists a Lusin topology with the given $σ$-algebra as the Borel $σ$-algebra so that $(ε, D(ε))$ 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.