RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 2012, Volume 92, Issue 3, Pages 410–416 (Mi mz9072)

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

DOI: https://doi.org/10.4213/mzm9072

Full text: PDF file (426 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2012, 92:3, 369–374

Bibliographic databases:

UDC: 517.9
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

Citation in format AMSBIB
\Bibitem{IvaPol12} \by G.~Ivanov, E.~S.~Polovinkin \paper A Generalization of the Set Averaging Theorem \jour Mat. Zametki \yr 2012 \vol 92 \issue 3 \pages 410--416 \mathnet{http://mi.mathnet.ru/mz9072} \crossref{https://doi.org/10.4213/mzm9072} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3201575} \zmath{https://zbmath.org/?q=an:1267.26010} \elib{http://elibrary.ru/item.asp?id=20731600} \transl \jour Math. Notes \yr 2012 \vol 92 \issue 3 \pages 369--374 \crossref{https://doi.org/10.1134/S000143461209009X} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000310228200009} \elib{http://elibrary.ru/item.asp?id=20497537} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84867925794}