Geodesic
On the closability and convergence of Dirichlet forms
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 270 (2010), pp. 220-225

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We construct a measure $\mu$ on $\mathbb R^2$ for which the gradient quadratic form is closable, whereas partial quadratic forms are not closable. We obtain new sufficient conditions for the Mosco convergence of Dirichlet forms. This gives effective conditions for the weak convergence of finite-dimensional distributions of diffusion processes. 
@article{TM_2010_270_a15,
     author = {O. V. Pugachev},
     title = {On the closability and convergence of {Dirichlet} forms},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {220--225},
     publisher = {mathdoc},
     volume = {270},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2010_270_a15/}
}
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O. V. Pugachev. On the closability and convergence of Dirichlet forms. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 270 (2010), pp. 220-225. http://geodesic.mathdoc.fr/item/TM_2010_270_a15/