Certain properties of triangular transformations of measures
We study the convergence of triangular mappings on R^n, i.e., mappings T such that the ith coordinate function Ti depends only on the variables x1, . . . ,xi. We show that, under broad assumptions, the inverse mapping to a canonical triangular transformation is canonical triangular as well. An exam...
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| Дата: | 2008 |
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| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2008
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/4540 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Certain properties of triangular transformations of measures / K.V. Medvedev // Theory of Stochastic Processes. — 2008. — Т. 14 (30), № 1. — С. 95–99. — Бібліогр.: 12 назв.— англ. |
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Medvedev, K.V. 2009-11-25T11:06:24Z 2009-11-25T11:06:24Z 2008 Certain properties of triangular transformations of measures / K.V. Medvedev // Theory of Stochastic Processes. — 2008. — Т. 14 (30), № 1. — С. 95–99. — Бібліогр.: 12 назв.— англ. 0321-3900 https://nasplib.isofts.kiev.ua/handle/123456789/4540 519.21 We study the convergence of triangular mappings on R^n, i.e., mappings T such that the ith coordinate function Ti depends only on the variables x1, . . . ,xi. We show 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. 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. en Інститут математики НАН України Certain properties of triangular transformations of measures Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Certain properties of triangular transformations of measures |
| spellingShingle |
Certain properties of triangular transformations of measures Medvedev, K.V. |
| title_short |
Certain properties of triangular transformations of measures |
| title_full |
Certain properties of triangular transformations of measures |
| title_fullStr |
Certain properties of triangular transformations of measures |
| title_full_unstemmed |
Certain properties of triangular transformations of measures |
| title_sort |
certain properties of triangular transformations of measures |
| author |
Medvedev, K.V. |
| author_facet |
Medvedev, K.V. |
| publishDate |
2008 |
| language |
English |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We study the convergence of triangular mappings on R^n, i.e., mappings T such that the ith coordinate function Ti depends only on the variables x1, . . . ,xi. We show 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.
|
| issn |
0321-3900 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/4540 |
| citation_txt |
Certain properties of triangular transformations of measures / K.V. Medvedev // Theory of Stochastic Processes. — 2008. — Т. 14 (30), № 1. — С. 95–99. — Бібліогр.: 12 назв.— англ. |
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2025-12-07T19:51:52Z |
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2025-12-07T19:51:52Z |
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1850880413282598912 |