Geodesic
Convergence of triangular transformations of measures
Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 1, pp. 145-150

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We prove that if a Borel probability measure $\mu$ on a countable product of Souslin spaces satisfies a certain condition of atomlessness, then for every Borel probability measure $\nu$ on this product, there exists a triangular mapping $T_{\mu,\nu}$ that takes $\mu$ to $\nu$. It is shown that in the case of metrizable spaces one can choose triangular mappings in such a way that convergence in variation of measures $\mu_n$ to $\mu$ and of measures $\nu_n$ to $\nu$ implies convergence of the mappings $T_{\mu_n,\nu_n}$ to $T_{\mu,\nu}$ in measure $\mu$.
Keywords: triangular mapping, conditional measure
Mots-clés : convergence in variation. 
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     author = {D. E. Aleksandrova},
     title = {Convergence of triangular transformations of measures},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {145--150},
     publisher = {mathdoc},
     volume = {50},
     number = {1},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2005_50_1_a7/}
}
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D. E. Aleksandrova. Convergence of triangular transformations of measures. Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 1, pp. 145-150. http://geodesic.mathdoc.fr/item/TVP_2005_50_1_a7/