Geodesic
Remarks on convergence of random processes in non-separable metric spaces and on the non-existence of a Borel measure for processes in~$C(0,\infty)$
Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 4, pp. 812-815

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Let a random element $\xi$ and random elements $\xi_n$ take values in a metric space $X$. Let $f$ be a measure and continuous functional on $X$. We discuss pecularities connected with convergence of the distributions of $f(\xi_n)$ to the distribution of $f(\xi)$ when the space $X$ is a non-separable one. 
@article{TVP_1973_18_4_a10,
     author = {A. A. Borovkov and A. I. Sakhanenko},
     title = {Remarks on convergence of random processes in non-separable metric spaces and on the non-existence of a {Borel} measure for processes in~$C(0,\infty)$},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {812--815},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1973_18_4_a10/}
}
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A. A. Borovkov; A. I. Sakhanenko. Remarks on convergence of random processes in non-separable metric spaces and on the non-existence of a Borel measure for processes in~$C(0,\infty)$. Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 4, pp. 812-815. http://geodesic.mathdoc.fr/item/TVP_1973_18_4_a10/