Geodesic
Series in multiplicative systems convergent to Denjoy-integrable functions
Sbornik. Mathematics, Tome 186 (1995) no. 12, pp. 1821-1842 Cet article a éte moissonné depuis la source Math-Net.Ru

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An example of a series in the Chrestenson–Levi system with $p_j=3$, $j=0,1,\dots$, with zero-convergent coefficients is constructed such that $\lim_{n\to\infty}S_{m_n}(x)=f(x)$ everywhere on $[0,1)$ for some function $f$ that is Denjoy integrable in the extended sense, but this series is not the Denjoy–Fourier series of $f$. A series in the Price system defined by a bounded sequence $\{p_j\}_{j=0}^\infty$ that converges everywhere on $[0,1)$ (with the possible exception of some countable set) to a function Denjoy integrable in the extended sense is proved to be Denjoy–Fourier series of this function. 
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V. A. Skvortsov; M. P. Koroleva. Series in multiplicative systems convergent to Denjoy-integrable functions. Sbornik. Mathematics, Tome 186 (1995) no. 12, pp. 1821-1842. http://geodesic.mathdoc.fr/item/SM_1995_186_12_a6/

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