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.
@article{bwmeta1.element.ojs-doi-10_17951_a_2017_71_1_73,
author = {Raymond Mortini},
title = {The Riemann-Cantor uniqueness theorem for unilateral trigonometric series via a special version of the Lusin-Privalov theorem},
journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica},
volume = {71},
year = {2017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2017_71_1_73}
}
Raymond Mortini. The Riemann-Cantor uniqueness theorem for unilateral trigonometric series via a special version of the Lusin-Privalov theorem. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 71 (2017) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2017_71_1_73/
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