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Funktsional'nyi Analiz i ego Prilozheniya, 2018, Volume 52, Issue 3, Pages 88–91
DOI: https://doi.org/10.4213/faa3502 (Mi faa3502) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Brief communications

On Minkowski Sums of Many Small Sets

M. M. Roginskayaab, V. S. Shul'manc

a Chalmers University of Technology
b University of Gothenburg, Department of Mathematical Sciences
c Vologda State University
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DOI: https://doi.org/10.4213/faa3502
Abstract: It is proved that a weakly closed subset of a Banach space is convex if and only if it can be represented as the sum of sets of arbitrarily small diameter.
Keywords: Minkowski addition, infinite divisibility, weak compactness, convexity.
Received: 22.06.2017
English version:
Functional Analysis and Its Applications, 2018, Volume 52, Issue 3, Pages 232–235
DOI: https://doi.org/10.1007/s10688-018-0233-4
Bibliographic databases:
Document Type: Article
UDC: 517+514
Language: Russian
Citation: M. M. Roginskaya, V. S. Shul'man, “On Minkowski Sums of Many Small Sets”, Funktsional. Anal. i Prilozhen., 52:3 (2018), 88–91; Funct. Anal. Appl., 52:3 (2018), 232–235
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
     
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