Geodesic
On unconditional convergence in the space $L_1$
Sbornik. Mathematics, Tome 23 (1974) no. 4, pp. 509-519 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@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
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/

[1] E. M. Nikishin, “Rezonansnye teoremy i nadlineinye operatory”, Uspekhi matem. nauk, XXV:6 (156) (1970), 129–191 | Zbl | Zbl

[2] S. Kachmazh, G. Shteingauz, Teoriya ortogonalnykh ryadov, Fizmatgiz, Moskva, 1958 | MR