Geodesic
The condition of almost everywhere convergence for a functional series with a weak analogue of the orthonormality property
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2016), pp. 18-24

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The almost everywhere convergence condition similar to the Menchoff–Rademacher condition is obtained for functional series with some weak analogue of the orthogonality property. As a corollary, the results of almost everywhere convergence of series with respect to Riesz systems, Hilbert and Bessel systems, and frames are obtained. 
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V. V. Galatenko; T. P. Lukashenko; V. A. Sadovnichii. The condition of almost everywhere convergence for a functional series with a weak analogue of the orthonormality property. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2016), pp. 18-24. http://geodesic.mathdoc.fr/item/VMUMM_2016_2_a2/