Matematicheskii Sbornik. Novaya Seriya
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. Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Sb. (N.S.), 1974, Volume 94(136), Number 4(8), Pages 540–550 (Mi msb3732)  

This article is cited in 1 scientific paper (total in 1 paper)

On unconditional convergence in the space $L_1$

B. S. Kashin


Abstract: The paper contains a proof of the following
Theorem. {\it Suppose $\sum_{k=1}^\infty f_k(x)$ converges unconditionally in $L_1[0,1]$. Then for any $\varepsilon>0$ there exists a set $E_\varepsilon\subset[0,1],$ $\mu E_\varepsilon>1-\varepsilon,$ such that $\sum_{k=1}^\infty f_k(x)$ converges unconditionally in $L_q(E_\varepsilon)$ for every $q<2$.}
This result is obtained as a corollary of a more general theorem.
Bibliography: 2 titles.

Full text: PDF file (838 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1974, 23:4, 509–519

Bibliographic databases:

UDC: 517.52
MSC: 40A05, 46E30
Received: 14.06.1973

Citation: B. S. Kashin, “On unconditional convergence in the space $L_1$”, Mat. Sb. (N.S.), 94(136):4(8) (1974), 540–550; Math. USSR-Sb., 23:4 (1974), 509–519

Citation in format AMSBIB
\Bibitem{Kas74}
\by B.~S.~Kashin
\paper On unconditional convergence in the space~$L_1$
\jour Mat. Sb. (N.S.)
\yr 1974
\vol 94(136)
\issue 4(8)
\pages 540--550
\mathnet{http://mi.mathnet.ru/msb3732}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=385537}
\zmath{https://zbmath.org/?q=an:0321.28005}
\transl
\jour Math. USSR-Sb.
\yr 1974
\vol 23
\issue 4
\pages 509--519
\crossref{https://doi.org/10.1070/SM1974v023n04ABEH002183}


Linking options:
  • http://mi.mathnet.ru/eng/msb3732
  • http://mi.mathnet.ru/eng/msb/v136/i4/p540

    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. Orno P., “Unconditionally Converging Series in Lp”, Proc. Amer. Math. Soc., 59:2 (1976), 252–254  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:345
    Full text:102
    References:38
    First page:3

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021