Denjoy–Luzin 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, http://gallica.bnf.fr/ark:/12148/bpt6k31089/f141 
• Hazewinkel, Michiel, ed. (2001), "Denjoy-Luzin theorem", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4, https://www.encyclopediaofmath.org/index.php?title=Main_Page 
• Luzin, N. N. (1912), "On the convergence of trigonometric series" (in Russian), Moskau Math. Samml. 28: 461–472