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arXiv · 1402.2429

Algorithmic aspects of Lipschitz functions

Cameron Freer·Bjørn Kjos-Hanssen·André Nies·Frank Stephan
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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 $L_1$-computable derivative is differentiable at z.

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Cameron Freer, Bjørn Kjos-Hanssen, André Nies, Frank Stephan. 2014-02-11. Algorithmic aspects of Lipschitz functions. https://doi.org/10.3233/com-14025

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