Geodesic
On the set of sums of a functional series
Matematičeskie zametki, Tome 7 (1970) no. 4, pp. 403-410

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A positive answer is given to one of Banach's problems on the set of sums of a functional series for various permutations of its terms. The problem is solved subject to one restricting condition, that $\sum_{n=1}^\infty f_n^2(x)\infty$ almost everywhere in $[0, 1]$. 
@article{MZM_1970_7_4_a4,
     author = {E. M. Nikishin},
     title = {On the set of sums of a functional series},
     journal = {Matemati\v{c}eskie zametki},
     pages = {403--410},
     publisher = {mathdoc},
     volume = {7},
     number = {4},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_7_4_a4/}
}
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E. M. Nikishin. On the set of sums of a functional series. Matematičeskie zametki, Tome 7 (1970) no. 4, pp. 403-410. http://geodesic.mathdoc.fr/item/MZM_1970_7_4_a4/