| Abstract: |
| We investigate topological properties of the Revuz correspondence. We provide necessary and sufficient conditions for the convergence of Revuz measures of finite energy integrals. In this setting, we show that the Revuz map, restricted to the class of finite energy integrals equipped with the norm induced by a Dirichlet form, is a homeomorphism when the space of positive continuous additive functionals is endowed with the topology induced by $L^2(P_{m+\kappa+\nu_0})$-norm together with the local uniform topology, where $m$ is the underlying measure, $\kappa$ is the killing measure and $\nu_0$ is an energy functional of a Hunt process. We also present a characterization of the Revuz correspondence in terms of killing of the process and further consider continuity properties of the Revuz correspondence for broader classes. |
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