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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