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This article is cited in 2 scientific papers (total in 2 papers)
A Generalization of the Set Averaging Theorem
G. Ivanov, E. S. Polovinkin Moscow Institute of Physics and Technology
Abstract:
We consider the possibility of generalizing the averaging theorem from the case of sets from $n$-dimensional Euclidean space to the case of sets from Banach spaces. The result is a cornerstone for constructing the theory of the Riemann integral for non-convex-valued multivalued mappings and for proving the convexity of this multivalued integral. We obtain a generalization of the averaging theorem to the case of sets from uniformly smooth Banach spaces as well as some corollaries.
Keywords:
set averaging theorem, $n$-dimensional Euclidean space, Banach space, Riemann integral, non-convex-valued multivalued mapping, convex compact set, Hausdorff metric.
Received: 30.08.2011 Revised: 12.12.2011
Citation:
G. Ivanov, E. S. Polovinkin, “A Generalization of the Set Averaging Theorem”, Mat. Zametki, 92:3 (2012), 410–416; Math. Notes, 92:3 (2012), 369–374
Linking options:
https://www.mathnet.ru/eng/mzm9072https://doi.org/10.4213/mzm9072 https://www.mathnet.ru/eng/mzm/v92/i3/p410
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Abstract page: | 561 | Full-text PDF : | 198 | References: | 54 | First page: | 36 |
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