Quasi-regular Dirichlet Forms and $L^p$ -resolvents on Measurable Spaces

Abstract

We prove that for any semi-Dirichlet form \({\left({\varepsilon,D{\left(\varepsilon\right)}}\right)}\) on a measurable Lusin space E there exists a Lusin topology with the given \(\sigma\)-algebra as the Borel \(\sigma\)-algebra so that \({\left({\varepsilon,D{\left(\varepsilon\right)}}\right)}\) 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.