Geodesic
Open Mappings of Probability Measures and the Skorokhod Representation Theorem
Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 1, pp. 3-27 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove that for the wide class of spaces X and Y (including completely regular Souslin spaces), every open surjective mapping $f\colon X\to Y$ induces the open mapping $\hat f\colon\mu\mapsto\mu\circ f^{-1}$ between the spaces of probability measures ${\mathcal P} (X)$ and ${\mathcal P} (Y)$. We discuss the existence of continuous inverse mappings for $\hat f$ and connections with the Skorokhod representation theorem and its generalizations.
Keywords: weak convergence of probability measures, Skorokhod representation, open mapping, continuous selection. 
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     title = {Open {Mappings} of {Probability} {Measures} and the {Skorokhod} {Representation} {Theorem}},
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V. I. Bogachev; A. V. Kolesnikov. Open Mappings of Probability Measures and the Skorokhod Representation Theorem. Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 1, pp. 3-27. http://geodesic.mathdoc.fr/item/TVP_2001_46_1_a0/