Denjoy–Luzin theorem

Denjoy–Luzin theorem For the Denjoy–Luzin theorem about functions of bounded variation, see Denjoy–Luzin–Saks theorem.

In matematica, the Denjoy–Luzin theorem, introduced independently by Denjoy (1912) and Luzin (1912) states that if a trigonometric series converges absolutely on a set of positive measure, then the sum of its coefficients converges absolutely, and in particular the trigonometric series converges absolutely everywhere.

References Denjoy, Arnaud (1912), "Sur l'absolue convergence des séries trigonométriques", C. R. Accad. Sci., 155: 135–136 "Denjoy-Luzin theorem", Enciclopedia della matematica, EMS Press, 2001 [1994] Luzin, N. N. (1912), "On the convergence of trigonometric series", Moskau Math. Samml. (in russo), 28: 461–472, JFM 43.0319.03 Questo articolo relativo all'analisi matematica è solo un abbozzo. Puoi aiutare Wikipedia espandendolo.

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