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Matematicheskie Zametki, 2012, Volume 92, Issue 3, Pages 410–416
DOI: https://doi.org/10.4213/mzm9072 (Mi mzm9072) 		 
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
Full-text PDF (426 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm9072
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
English version:
Mathematical Notes, 2012, Volume 92, Issue 3, Pages 369–374
DOI: https://doi.org/10.1134/S000143461209009X
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
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
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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