Quasi-Homeomorphisms and Measures of Finite Energy Integrals of Generalized Dirichlet Forms

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 F^ is associated with a measure of finite energy integral. Consequently, we prove that a Borel set B is .-exceptional if and only if . (B) = 0 for any measure . of finite energy integral.