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Teor. Veroyatnost. i Primenen., 2001, Volume 46, Issue 1, Pages 3–27 (Mi tvp3944)  

This article is cited in 6 scientific papers (total in 6 papers)

Open Mappings of Probability Measures and the Skorokhod Representation Theorem

V. I. Bogachev, A. V. Kolesnikov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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.

DOI: https://doi.org/10.4213/tvp3944

Full text: PDF file (3179 kB)

English version:
Theory of Probability and its Applications, 2002, 46:1, 20–38

Bibliographic databases:

Received: 09.06.1999

Citation: V. I. Bogachev, A. V. Kolesnikov, “Open Mappings of Probability Measures and the Skorokhod Representation Theorem”, Teor. Veroyatnost. i Primenen., 46:1 (2001), 3–27; Theory Probab. Appl., 46:1 (2002), 20–38

Citation in format AMSBIB
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\paper Open Mappings of Probability Measures and the Skorokhod Representation Theorem
\jour Teor. Veroyatnost. i Primenen.
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\pages 3--27
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\jour Theory Probab. Appl.
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\pages 20--38
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Banakh T.O., Bogachev V.I., Kolesnikov A.V., “Topological spaces with Prokhorov and Skorokhod properties”, Dokl. Math., 64:2 (2001), 244–247  mathnet  mathscinet  zmath  isi
    2. Banakh T., Chigogidze A., Fedorchuk V., “On spaces of $\sigma$-additive probability measures”, Topology Appl., 133:2 (2003), 139–155  crossref  mathscinet  zmath  isi  scopus
    3. Kolesnikov A.V., “Convexity inequalities and optimal transport of infinite-dimensional measures”, J. Math. Pures Appl. (9), 83:11 (2004), 1373–1404  crossref  mathscinet  zmath  isi  scopus
    4. V. I. Bogachev, A. V. Kolesnikov, “Integrability of absolutely continuous measure transformations and applications to optimal transportation”, Theory Probab. Appl., 50:3 (2006), 367–385  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. Valov V., “Probability measures and Milyutin maps between metric spaces”, J. Math. Anal. Appl., 350:2 (2009), 723–730  crossref  mathscinet  zmath  isi  elib  scopus
    6. Roininen L., Piiroinen P., Lehtinen M., “Constructing Continuous Stationary Covariances as Limits of the Second-Order Stochastic Difference Equations”, Inverse Probl. Imaging, 7:2 (2013), 611–647  crossref  mathscinet  zmath  isi  elib  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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