Geodesic
On unconditional convergence in the space~$L_1$
Sbornik. Mathematics, Tome 23 (1974) no. 4, pp. 509-519

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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 $q2$.} This result is obtained as a corollary of a more general theorem. Bibliography: 2 titles. 
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     author = {B. S. Kashin},
     title = {On unconditional convergence in the space~$L_1$},
     journal = {Sbornik. Mathematics},
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     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {1974},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1974_23_4_a2/}
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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/