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Certain properties of triangular
transformations of measures
Kirill V. Medvedev Faculty of Mechanics and Mathematics Moscow State University, Moscow 119992, Russia
Аннотация:
We study the convergence of triangular mappings on ${\mathbb R}^n,$ i.e., mappings $T$ such that
the $i$th coordinate function $T_i$ depends only on the variables $x_1,\ldots,x_i.$ Weshow
that, under broad assumptions, the inverse mapping to a canonical triangular transformation is canonical triangular as well. An example is constructed showing that
the convergence in variation of measures is not sufficient for the convergence almost
everywhere of the associated canonical triangular transformations. Finally, we show
that the weak convergence of absolutely continuous convex measures to an absolutely
continuous measure yields the convergence in variation. As a corollary, this implies
the convergence in measure of the associated canonical triangular transformations.
Ключевые слова:
Triangular transformations, weak convergence of measures, convex measures.
Финансовая поддержка |
Номер гранта |
Deutsche Forschungsgemeinschaft  |
436 RUS 113/343/0(R) |
Partially supported by the RFBR projects 07-01-00536 and GFEN-06-01-39003, the DFG grant 436
RUS 113/343/0(R), and the INTAS project 05-109-4856. |
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Тип публикации:
Статья
MSC: 28C20, 46G12, 60B11
Язык публикации: английский
Образец цитирования:
Kirill V. Medvedev, “Certain properties of triangular
transformations of measures”, Theory Stoch. Process., 14(30):1 (2008), 95–99
Цитирование в формате AMSBIB
\RBibitem{Med08}
\by Kirill~V.~Medvedev
\paper Certain properties of triangular
transformations of measures
\jour Theory Stoch. Process.
\yr 2008
\vol 14(30)
\issue 1
\pages 95--99
\mathnet{http://mi.mathnet.ru/thsp133}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2479710}
\zmath{https://zbmath.org/?q=an:1199.28047}
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http://mi.mathnet.ru/thsp133 http://mi.mathnet.ru/rus/thsp/v14/i1/p95
Citing articles on Google Scholar:
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English citations
Related articles on Google Scholar:
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