As noted in class, we gave Fejér's original proof of his theorem on the Cesàro summability of a Fourier series of a continuous function (except for the fact the he assumed the function to be even and, thus, its Fourier series contains only cosines).
Fejér's theorem was published in Comptes Rendus Hebdomadaries, Seances de l’Academie de Sciences, Paris 131 (1900), and you can find the paper here: Sur les fonctions bornées et intégrables.
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