Work

On sets where $\operatorname{lip}f$ is infinite for monotone continuous functions

Year: 2025

Type: article

Abstract: 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.

Source: Documenta Mathematica

DOI: 10.4171/dm/1017

Authors: Martin Rmoutil, Thomas Zürcher

Institutions: Charles University, University of Silesia in Katowice

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: University of Warwick, European Commission, Uniwersytet Śląski w Katowicach, FP7 Ideas: European Research Council

Awards: G3207356259, Local Structure of Sets, Measures and Currents, G7546946110, G896728979