Geodesic
Summability of series with respect to a Haar system by the $(C,1)$ method
Matematičeskie zametki, Tome 15 (1974) no. 3, pp. 393-404 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a Haar-system series we prove that if the lower bound of the $(C,1)$ means of the series is larger than $-\infty$ on a set $E$ of positive measure, then the series converges to a finite function almost everywhere on $E$; from this it follows that Haar-system series are not summable by the $(C,1)$ method to $+\infty$ on sets of positive measure. 
@article{MZM_1974_15_3_a5,
     author = {L. A. Shaginyan},
     title = {Summability of series with respect to {a~Haar} system by the $(C,1)$ method},
     journal = {Matemati\v{c}eskie zametki},
     pages = {393--404},
     year = {1974},
     volume = {15},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a5/}
}
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L. A. Shaginyan. Summability of series with respect to a Haar system by the $(C,1)$ method. Matematičeskie zametki, Tome 15 (1974) no. 3, pp. 393-404. http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a5/