RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
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. Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Sb., 2008, Volume 199, Number 6, Pages 49–84 (Mi msb3845)  

This article is cited in 5 scientific papers (total in 5 papers)

Classification of Borel sets and functions for an arbitrary space

V. K. Zakharova, T. V. Rodionovb

a Centre for New Information Technologies, Moscow State University
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: For Borel functions on a perfect normal space and a perfect topological space there are two Baire convergence classifications: one due to Lebesgue and Hausdorff and the other due to Banach. However, neither classification is valid for an arbitrary topological space. In this paper the Baire convergence classification of Borel functions on an arbitrary space is given. This classification of Borel functions uses two classifications of Borel sets: one generalises the Young-Hausdorff classification for a perfect space and the other is new.
Bibliography: 17 titles.

DOI: https://doi.org/10.4213/sm3845

Full text: PDF file (769 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2008, 199:6, 833–869

Bibliographic databases:

UDC: 517.517+510.225+517.518.26
MSC: Primary 26A21; Secondary 54C50, 54H05, 03E15
Received: 26.02.2007 and 04.10.2007

Citation: V. K. Zakharov, T. V. Rodionov, “Classification of Borel sets and functions for an arbitrary space”, Mat. Sb., 199:6 (2008), 49–84; Sb. Math., 199:6 (2008), 833–869

Citation in format AMSBIB
\Bibitem{ZakRod08}
\by V.~K.~Zakharov, T.~V.~Rodionov
\paper Classification of Borel sets and functions for an arbitrary space
\jour Mat. Sb.
\yr 2008
\vol 199
\issue 6
\pages 49--84
\mathnet{http://mi.mathnet.ru/msb3845}
\crossref{https://doi.org/10.4213/sm3845}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2435273}
\zmath{https://zbmath.org/?q=an:1177.54008}
\elib{http://elibrary.ru/item.asp?id=20359333}
\transl
\jour Sb. Math.
\yr 2008
\vol 199
\issue 6
\pages 833--869
\crossref{https://doi.org/10.1070/SM2008v199n06ABEH003944}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000259031600009}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-52049087857}


Linking options:
  • http://mi.mathnet.ru/eng/msb3845
  • https://doi.org/10.4213/sm3845
  • http://mi.mathnet.ru/eng/msb/v199/i6/p49

    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

    This publication is cited in the following articles:
    1. V. K. Zakharov, A. V. Mikhalev, T. V. Rodionov, “The Riesz–Radon–Fréchet problem of characterization of integrals”, Russian Math. Surveys, 65:4 (2010), 741–765  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. V. K. Zakharov, A. V. Mikhalev, T. V. Rodionov, “Characterization of Radon integrals as linear functionals”, J. Math. Sci., 185:2 (2012), 233–281  mathnet  crossref  mathscinet
    3. T.V. Rodionov, V.K. Zakharov, “A fine correlation between Baire and Borel functional hierarchies”, Acta Math. Hung., 142:2 (2014), 384–402  crossref  mathscinet  zmath  isi  elib  scopus
    4. V. K. Zakharov, T. V. Rodionov, “Naturalness of the Class of Lebesgue–Borel–Hausdorff Measurable Functions”, Math. Notes, 95:4 (2014), 500–508  mathnet  crossref  crossref  mathscinet  isi  elib
    5. V. K. Zakharov, A. V. Mikhalev, T. V. Rodionov, “Descriptive spaces and proper classes of functions”, J. Math. Sci., 213:2 (2016), 163–200  mathnet  crossref  mathscinet
  • Математический сборник Sbornik: Mathematics (from 1967)
    Number of views:
    This page:378
    Full text:106
    References:38
    First page:8

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019