Denjoy–Luzin theorem

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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.


  • Denjoy, Arnaud (1912), "Sur l'absolue convergence des séries trigonométriques", C. R. Acad. Sci., 155: 135–136 
  • Hazewinkel, Michiel, ed. (2001) [1994], "Denjoy–Luzin_theorem", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, 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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