RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Funktsional. Anal. i Prilozhen.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Funktsional. Anal. i Prilozhen., 2008, Volume 42, Issue 2, Pages 89–94 (Mi faa2908)  

Brief communications

Continuous Selections as Parametrically Defined Integrals

P. V. Semenov

Moscow City Pedagogical University, Mathematical Department

Abstract: An analog of the classical Michael theorem on continuous single-valued selections of lower semicontinuous maps whose values are closed and convex in a Fréchet space is proved for maps into metrizable (non-locally-convex) vector spaces. It turns out that, instead of the local convexity of the whole space containing these values, it is sufficient to require that the family of values of the map be \del{pointwise} uniformly locally convex. In contrast to the standard selection theorems, the proof bypasses the process of successively improving the approximations, and the desired selection is constructed as the result of pointwise integration with respect to a suitable probability distribution.

Keywords: continuous selection, convex-valued map, non-locally-convex vector space, paracompact space, probability measure

DOI: https://doi.org/10.4213/faa2908

Full text: PDF file (177 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 2008, 42:2, 155–159

Bibliographic databases:

UDC: 515.12+517.982.252
Received: 15.01.2007

Citation: P. V. Semenov, “Continuous Selections as Parametrically Defined Integrals”, Funktsional. Anal. i Prilozhen., 42:2 (2008), 89–94; Funct. Anal. Appl., 42:2 (2008), 155–159

Citation in format AMSBIB
\Bibitem{Sem08}
\by P.~V.~Semenov
\paper Continuous Selections as Parametrically Defined Integrals
\jour Funktsional. Anal. i Prilozhen.
\yr 2008
\vol 42
\issue 2
\pages 89--94
\mathnet{http://mi.mathnet.ru/faa2908}
\crossref{https://doi.org/10.4213/faa2908}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2438024}
\zmath{https://zbmath.org/?q=an:1161.54009}
\transl
\jour Funct. Anal. Appl.
\yr 2008
\vol 42
\issue 2
\pages 155--159
\crossref{https://doi.org/10.1007/s10688-008-0024-4}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000257324700012}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-46249105254}


Linking options:
  • http://mi.mathnet.ru/eng/faa2908
  • https://doi.org/10.4213/faa2908
  • http://mi.mathnet.ru/eng/faa/v42/i2/p89

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
    Number of views:
    This page:370
    Full text:120
    References:41
    First page:14

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020