Geodesic
Equimeasurable sets and cylindrical measures
Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 4, pp. 731-740

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We obtain a characterization of equimeasurable sets in the space $S(\Omega ,\Sigma,\mathbf{P})$ in terms of the coincidence of convergence in probability and almost sure convergence. The notion of an equimeasurable set is used to obtain criteria for extending a cylindrical measure to a Radon measure and also to establish a criterion of the existence of continuous trajectories of a linear random function on an absolutely convex weak compact set.
Keywords: equimeasurable sets, cylindrical measures, convergence in probability, almost sure convergence. 
@article{TVP_1995_40_4_a1,
     author = {Yu. N. Vladimirskii},
     title = {Equimeasurable sets and cylindrical measures},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {731--740},
     publisher = {mathdoc},
     volume = {40},
     number = {4},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1995_40_4_a1/}
}
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Yu. N. Vladimirskii. Equimeasurable sets and cylindrical measures. Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 4, pp. 731-740. http://geodesic.mathdoc.fr/item/TVP_1995_40_4_a1/