Geodesic
On the uniqueness of a Haar series that converges with respect to subsequences of partial sums
Matematičeskie zametki, Tome 4 (1968) no. 6, pp. 707-714 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove the existence of two different series in the Haar system for which the subsequences of partial sums converge to the same $D$-integrable function everywhere on $[0,1]$. 
@article{MZM_1968_4_6_a10,
     author = {V. A. Skvortsov},
     title = {On the uniqueness of {a~Haar} series that converges with respect to subsequences of partial sums},
     journal = {Matemati\v{c}eskie zametki},
     pages = {707--714},
     year = {1968},
     volume = {4},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_6_a10/}
}
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V. A. Skvortsov. On the uniqueness of a Haar series that converges with respect to subsequences of partial sums. Matematičeskie zametki, Tome 4 (1968) no. 6, pp. 707-714. http://geodesic.mathdoc.fr/item/MZM_1968_4_6_a10/