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

Authors:	Lucian Beznea Nicu Boboc Michael Röckner

Institution:	1. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, RO-014700, Bucharest, Romania 2. Faculty of Mathematics and Informatics, University of Bucharest, str. Academiei 14, RO-010014, Bucharest, Romania 3. Fakult?t für Mathematik, Universit?t Bielefeld, Postfach 100 131, D-33501, Bielefeld, Germany

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 -resolvents is proven.

Keywords:	semi-Dirichlet form -resolvent" target="_blank">gif" alt="$L^p$" align="middle" border="0">-resolvent quasi-regularity right process
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