On sets where $\operatorname{lip}f$ is infinite for monotone continuous functions
Given an F_{\sigma\delta} 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.
Authors
- Thomas Zürcher (ORCID: https://orcid.org/0000-0001-9179-9521)
- Martin Rmoutil (ORCID: https://orcid.org/0000-0002-1340-4974)
Institutions
- Charles University (CZ)
Publication Details
- Journal
- Documenta Mathematica
- Published
- 2025-08-26
- DOI
- https://doi.org/10.4171/dm/1017
- Citations
- 1
- Primary Topic
- Advanced Banach Space Theory
- Type
- article
- Field-Weighted Citation Impact
- 3.69
Funders
- University of Warwick
- European Commission
- Uniwersytet Śląski w Katowicach