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

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 $\sigma$-algebra as the Borel $\sigma$-algebra so that $(\epsilon, D(\epsilon))$becomesquasi-regular\mathrm{.}Howeveronehastoenlarge$E$ by a zero set. More generally a corresponding result for arbitrary $L^p$-resolvents is proven.