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