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

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