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Труды Петрозаводского государственного университета. Математика, 2005, выпуск 12, страницы 3–12
(Mi pa57)
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On metric space valued functions of bounded essential variation
M. Balcerzaka, M. Małolepszyb a Technical University of Łódź, Institute of Mathematics
b Institute of Physics Lodz, University of Technology
Аннотация:
Let $\emptyset \ne T \subset \mathbb{R}$ and let $X$ be a metric space. For an ideal $\mathcal{J}\subset \mathcal{P}(T)$ and a function $f:T\to X$, we define the essential variation $V^{\mathcal{J}}_{ess}(f, T)$ as the in mum of all variations $V (g, T)$ where $g:T\to X, g = f$ on $T\setminus E$, and $E \in \mathcal{J}$. We show that if $X$ is complete then the essential variation of $f$ is equal to inf$\{V (f; T\setminus E) : E \in \mathcal{J}\}$. This extends former theorems of that type. We list some consequences that are analogues to the recent results by Chistyakov. Some examples of di erent kinds of essential variation are also investigated.
Образец цитирования:
M. Balcerzak, M. Małolepszy, “On metric space valued functions of bounded essential variation”, Труды ПГУ. Математика, 2005, no. 12, 3–12
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/pa57 https://www.mathnet.ru/rus/pa/y2005/i12/p3
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Страница аннотации: | 58 | PDF полного текста: | 33 |
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