Geodesic
On the de la Vall\'e-Poussin theorem on the~uniqueness of the~trigonometric series representing a~function
Sbornik. Mathematics, Tome 187 (1996) no. 5, pp. 767-784

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The de la Vallé-Poussin theorem states that if a trigonometric series converges to a finite integrable function $f$ everywhere outside a countable set $E$, then it is the Fourier series of $f$. In this paper the theorem is shown to hold also if the exceptional set $E$ is a union of finitely many $H$-sets. 
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     author = {N. N. Kholshchevnikova},
     title = {On the de la {Vall\'e-Poussin} theorem on the~uniqueness of the~trigonometric series representing a~function},
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N. N. Kholshchevnikova. On the de la Vall\'e-Poussin theorem on the~uniqueness of the~trigonometric series representing a~function. Sbornik. Mathematics, Tome 187 (1996) no. 5, pp. 767-784. http://geodesic.mathdoc.fr/item/SM_1996_187_5_a7/