Geodesic
On a property of complete orthonormal systems
Matematičeskie zametki, Tome 17 (1975) no. 5, pp. 681-690 
N. B. Pogosyan. On a property of complete orthonormal systems. Matematičeskie zametki, Tome 17 (1975) no. 5, pp. 681-690. http://geodesic.mathdoc.fr/item/MZM_1975_17_5_a0/
@article{MZM_1975_17_5_a0,
     author = {N. B. Pogosyan},
     title = {On a~property of complete orthonormal systems},
     journal = {Matemati\v{c}eskie zametki},
     pages = {681--690},
     year = {1975},
     volume = {17},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_5_a0/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we establish a necessary and sufficient condition for orthonormal systems, subject to which there exist rearranged series $\Sigma_\sigma a_n\varphi_n(x)$ converging almost everywhere to functions $h(x)\overline\in L_2[0,1]$. In particular, we show, for an arbitrary complete orthonormal system, that such series exist.