Sbornik. Mathematics, Tome 23 (1974) no. 4, pp. 509-519
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B. S. Kashin. On unconditional convergence in the space $L_1$. Sbornik. Mathematics, Tome 23 (1974) no. 4, pp. 509-519. http://geodesic.mathdoc.fr/item/SM_1974_23_4_a2/
@article{SM_1974_23_4_a2,
author = {B. S. Kashin},
title = {On unconditional convergence in the space~$L_1$},
journal = {Sbornik. Mathematics},
pages = {509--519},
year = {1974},
volume = {23},
number = {4},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1974_23_4_a2/}
}
TY - JOUR
AU - B. S. Kashin
TI - On unconditional convergence in the space $L_1$
JO - Sbornik. Mathematics
PY - 1974
SP - 509
EP - 519
VL - 23
IS - 4
UR - http://geodesic.mathdoc.fr/item/SM_1974_23_4_a2/
LA - en
ID - SM_1974_23_4_a2
ER -
%0 Journal Article
%A B. S. Kashin
%T On unconditional convergence in the space $L_1$
%J Sbornik. Mathematics
%D 1974
%P 509-519
%V 23
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1974_23_4_a2/
%G en
%F SM_1974_23_4_a2
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.
