On mappings of bounded variation |
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Authors: | V V Chistyakov |
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Affiliation: | (1) Department of Mathematics, University of Nizhny Novgorod, 23 Gagarin Avenue, 603600 Nizhny Novgorod, Russia |
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Abstract: | We present the properties of mappings of bounded variation defined on a subset of the real line with values in metric and
normed spaces and show that major aspects of the theory of realvalued functions of bounded variation remains valid in this
case. In particular, we prove the structure theorem and obtain the continuity properties of these mappings as well as jump
formulas for the variation. We establish the existence of Lipschitz continuous geodesic paths and prove an analog of the well-known
Helly selection principle. For normed space-valued smooth mappings we obtain the usual integral formula for the variation
without the completeness assumption on the space of values. As an application of our theory we show that compact set-valued
mappings (=multifunctions) of bounded variation admit regular selections of bounded variation.
Partially supported by the Russian Foundation for Fundamental Research, Grant No. 96-01-00278. |
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Keywords: | 1991 Mathematics Subject Classification" target="_blank">1991 Mathematics Subject Classification 26A45 54C60 54C65 49J45 |
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