Denjoy–Luzin–Saks_theorem

Denjoy–Luzin–Saks theorem

Denjoy–Luzin–Saks theorem

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Not to be confused with Denjoy–Luzin theorem.

In mathematics, the Denjoy–Luzin–Saks theorem states that a function of generalized bounded variation in the restricted sense has a derivative almost everywhere, and gives further conditions of the set of values of the function where the derivative does not exist. N. N. Luzin and A. Denjoy proved a weaker form of the theorem, and Saks (1937, theorem 7.2, page 230) later strengthened their theorem.

References

  • Saks, Stanisław (1937), Theory of the Integral, Monografie Matematyczne, vol. 7 (2nd ed.), Warszawa-Lwów: G.E. Stechert & Co., JFM 63.0183.05, Zbl 0017.30004, archived from the original on 2006-12-12


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