This article is cited in 5 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.

Received: 01.07.2004

DOI: 10.4213/tvp162

 English version: Theory of Probability and its Applications, 2006, 50:1, 113–118

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