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

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

2005-12-22

arxiv.org/abs/math/0512524v1

Mathematics

Probability

14 pages, to appear in Potential Analysis

Scientific paper

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.

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