Geodesic
Open Mappings of Probability Measures and the Skorokhod Representation Theorem
Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 1, pp. 3-27

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TVP_2001_46_1_a0,
     author = {V. I. Bogachev and A. V. Kolesnikov},
     title = {Open {Mappings} of {Probability} {Measures} and the {Skorokhod} {Representation} {Theorem}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {3--27},
     publisher = {mathdoc},
     volume = {46},
     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2001_46_1_a0/}
}
TY  - JOUR
AU  - V. I. Bogachev
AU  - A. V. Kolesnikov
TI  - Open Mappings of Probability Measures and the Skorokhod Representation Theorem
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2001
SP  - 3
EP  - 27
VL  - 46
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_2001_46_1_a0/
LA  - ru
ID  - TVP_2001_46_1_a0
ER  - 
%0 Journal Article
%A V. I. Bogachev
%A A. V. Kolesnikov
%T Open Mappings of Probability Measures and the Skorokhod Representation Theorem
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2001
%P 3-27
%V 46
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_2001_46_1_a0/
%G ru
%F TVP_2001_46_1_a0
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/