# Denjoy–Luzin theorem

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

In mathematics, 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. Acad. Sci., 155: 135–136 "Denjoy-Luzin theorem", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Luzin, N. N. (1912), "On the convergence of trigonometric series", Moskau Math. Samml. (in Russian), 28: 461–472, JFM 43.0319.03 This mathematical analysis–related article is a stub. You can help Wikipedia by expanding it.

Categories: Fourier seriesTheorems in analysisMathematical analysis stubs

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