Geodesic
On the closability and convergence of Dirichlet forms
Informatics and Automation, 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{TRSPY_2010_270_a15,
     author = {O. V. Pugachev},
     title = {On the closability and convergence of {Dirichlet} forms},
     journal = {Informatics and Automation},
     pages = {220--225},
     publisher = {mathdoc},
     volume = {270},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2010_270_a15/}
}
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O. V. Pugachev. On the closability and convergence of Dirichlet forms. Informatics and Automation, Differential equations and dynamical systems, Tome 270 (2010), pp. 220-225. http://geodesic.mathdoc.fr/item/TRSPY_2010_270_a15/