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This article is cited in 4 scientific papers (total in 4 papers)
Short Communications
Convergence of triangular transformations of measures
D. E. Aleksandrova M. V. Lomonosov Moscow State University
Abstract:
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, convergence in variation.
DOI:
https://doi.org/10.4213/tvp162
Full text:
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English version:
Theory of Probability and its Applications, 2006, 50:1, 113–118
Bibliographic databases:
Received: 01.07.2004
Citation:
D. E. Aleksandrova, “Convergence of triangular transformations of measures”, Teor. Veroyatnost. i Primenen., 50:1 (2005), 145–150; Theory Probab. Appl., 50:1 (2006), 113–118
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/tvp162https://doi.org/10.4213/tvp162 http://mi.mathnet.ru/eng/tvp/v50/i1/p145
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This publication is cited in the following articles:
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V. I. Bogachev, A. V. Kolesnikov, K. V. Medvedev, “Triangular transformations of measures”, Sb. Math., 196:3 (2005), 309–335
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V. I. Bogachev, A. V. Kolesnikov, “Nonlinear transformations of convex measures”, Theory Probab. Appl., 50:1 (2006), 34–52
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Kirill V. Medvedev, “Certain properties of triangular
transformations of measures”, Theory Stoch. Process., 14(30):1 (2008), 95–99
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Zhdanov R.I., “Continuity and differentiability of triangular mappings”, Dokl. Math., 82:2 (2010), 741–745
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