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This article is cited in 19 scientific papers (total in 19 papers)
Multi-Valued Mappings of Bounded Generalized Variation
V. V. Chistyakov N. I. Lobachevski State University of Nizhni Novgorod
Abstract:
We study the mappings taking real intervals into metric spaces and possessing a bounded generalized variation in the sense of Jordan–Riesz–Orlicz. We establish some embeddings of function spaces, the structure of the mappings, the jumps of the variation, and the Helly selection principle. We show that a compact-valued multi-valued mapping of bounded generalized variation with respect to the Hausdorff metric has a regular selection of bounded generalized variation. We prove the existence of selections preserving the properties of multi-valued mappings that are defined on the direct product of an interval and a topological space, have a bounded generalized variation in the first variable, and are upper semicontinuous in the second variable.
Received: 02.02.2000 Revised: 09.02.2001
Citation:
V. V. Chistyakov, “Multi-Valued Mappings of Bounded Generalized Variation”, Mat. Zametki, 71:4 (2002), 611–632; Math. Notes, 71:4 (2002), 556–575
Linking options:
https://www.mathnet.ru/eng/mzm372https://doi.org/10.4213/mzm372 https://www.mathnet.ru/eng/mzm/v71/i4/p611
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