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., 1990, Volume 181, Number 3, Pages 402–415 (Mi msb1174)  

Existence of untrivial compact Tchebycheff sets in the spaces $L_\varphi$

D.-A. G. Kamuntavichius

Vilnius University

Abstract: It is proved that if $(T,\Omega,\mu)$ is a nonatomic measure space and $\varphi$ an even function nondecreasing on $[0,\infty)$ and such that $\varphi(0)=0$, $\varphi(u)>0$ for $u>0$, and $\varphi(u_1+u_2)<\varphi(u_1)+\varphi(u_2)$ for all $u_1,u_2>0$, then the space $L_\varphi(T,\Omega,\mu)$ does not contain boundedly compact Tchebycheff sets with more than one point.

Full text: PDF file (1284 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1991, 69:2, 431–444

Bibliographic databases:

UDC: 517.518.8
MSC: Primary 46E30, 46B20; Secondary 46A50
Received: 25.11.1988

Citation: D. G. Kamuntavichius, “Existence of untrivial compact Tchebycheff sets in the spaces $L_\varphi$”, Mat. Sb., 181:3 (1990), 402–415; Math. USSR-Sb., 69:2 (1991), 431–444

Citation in format AMSBIB
\Bibitem{Kam90}
\by D.~G.~Kamuntavichius
\paper Existence of untrivial compact Tchebycheff sets in the spaces~$L_\varphi$
\jour Mat. Sb.
\yr 1990
\vol 181
\issue 3
\pages 402--415
\mathnet{http://mi.mathnet.ru/msb1174}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1049997}
\zmath{https://zbmath.org/?q=an:0753.41031|0719.41042}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1991SbMat..69..431K}
\transl
\jour Math. USSR-Sb.
\yr 1991
\vol 69
\issue 2
\pages 431--444
\crossref{https://doi.org/10.1070/SM1991v069n02ABEH002114}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1991GB41500007}


Linking options:
  • http://mi.mathnet.ru/eng/msb1174
  • http://mi.mathnet.ru/eng/msb/v181/i3/p402

    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
  • Математический сборник - 1989–1990 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:144
    Full text:38
    References:39
    First page:1

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