Geodesic
The Riemann-Cantor uniqueness theorem for unilateral trigonometric series via a special version of the Lusin-Privalov theorem
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 71 (2017) no. 1.

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Using Baire's theorem, we give a very simple proof of a special version of the Lusin-Privalov theorem and deduce via Abel's  theorem the  Riemann-Cantor theorem on the uniqueness of the coefficients of pointwise convergent unilateral trigonometric series.
Keywords: Boundary behaviour of analytic functions, trigonometric series 
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Mortini, Raymond. The Riemann-Cantor uniqueness theorem for unilateral trigonometric series via a special version of the Lusin-Privalov theorem. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 71 (2017) no. 1. http://geodesic.mathdoc.fr/item/AUM_2017_71_1_a7/

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