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.
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Beznea, L., Boboc, N. & Röckner, M. Quasi-regular Dirichlet Forms and \(L^p\)-resolvents on Measurable Spaces. Potential Anal 25, 269–282 (2006). https://doi.org/10.1007/s11118-006-9016-2
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DOI: https://doi.org/10.1007/s11118-006-9016-2