4 ALGORITHMIC ASPECTS OF LIPSCHITZ FUNCTIONS
Cameron E. Freer, Bjørn Kjos-hanssen, André Nies, Frank Stephan · 2013
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. Furthermore, a real z is Schnorr random if and only if every Lipschitz function with L1-computable derivative is differentiable at z. For the implications from left to right we rely on literature results. The converse implications are obtained by novel constructions of computable Lipschitz functions from randomness tests. 1.