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
- Hazewinkel, Michiel, ed. (2001), "Denjoy–Luzin_theorem", Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4
- Luzin, N. N. (1912), "On the convergence of trigonometric series", Moskau Math. Samml. (in Russian), 28: 461–472, JFM 43.0319.03
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