Quasi-Homeomorphisms and Measures of Finite Energy Integrals of Generalized Dirichlet Forms |
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Authors: | Wei Sun |
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Institution: | (1) Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, 100080, P. R. China, E-mail: sunw@amath4.amt.ac.cn, CN |
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Abstract: | We introduce the quasi-homeomorphisms of generalized Dirichlet forms and prove that any quasi-regular generalized Dirichlet
form is quasi-homeomorphic to a semi-regular generalized Dirichlet form. Moreover, we apply this quasi-homeomorphism method
to study the measures of finite energy integrals of generalized Dirichlet forms. We show that any 1-coexcessive function which
is dominated by a function in is associated with a measure of finite energy integral. Consequently, we prove that a Borel set B is ɛ-exceptional if and only if μ (B) = 0 for any measure μ of finite energy integral.
Received May 28, 1999, Revised September 8, 1999, Accepted December 10, 1999 |
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Keywords: | Generalized Dirichlet form Quasi-homeomorphism Measure of finite energy integral |
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