English

Algorithmic aspects of Lipschitz functions

Logic 2014-05-15 v1 Classical Analysis and ODEs

Abstract

We characterize the variation functions of computable Lipschitz functions. We show that a real z is computably random if and only if every computable Lipschitz function is differentiable at z. Beyond these principal results, we show that a real z is Schnorr random if and only if every Lipschitz function with L1L_1-computable derivative is differentiable at z.

Cite

@article{arxiv.1402.2429,
  title  = {Algorithmic aspects of Lipschitz functions},
  author = {Cameron Freer and Bjørn Kjos-Hanssen and André Nies and Frank Stephan},
  journal= {arXiv preprint arXiv:1402.2429},
  year   = {2014}
}

Comments

18 pages

R2 v1 2026-06-22T03:05:30.588Z