English

On sets where lip(f) is infinite for monotone continuous functions

Classical Analysis and ODEs 2024-01-30 v1

Abstract

Given an F-sigma-delta subset A of the real line R of Lebesgue measure zero, we construct a monotone absolutely continuous function f from R to R such that the little Lipschitz constant of f is equal to infinity exactly at points of A.

Keywords

Cite

@article{arxiv.2401.15388,
  title  = {On sets where lip(f) is infinite for monotone continuous functions},
  author = {Martin Rmoutil and Thomas Zürcher},
  journal= {arXiv preprint arXiv:2401.15388},
  year   = {2024}
}