On sets where is infinite for monotone continuous functions

  • Martin Rmoutil

    Charles University, Praha, Czech Republic
  • Thomas Zürcher

    Uniwersytet Śląski, Katowice, Poland
On sets where $\operatorname{lip}f$ is infinite for monotone continuous functions cover
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Abstract

Given an subset in the real line of measure zero, we explain how to obtain a nondecreasing absolutely continuous function such that the derivative is infinite at every point in the set and the little Lipschitz constant (the lower scaled oscillation) is finite at each point outside the set.

Cite this article

Martin Rmoutil, Thomas Zürcher, On sets where is infinite for monotone continuous functions. Doc. Math. (2025), published online first

DOI 10.4171/DM/1017