Points of non-differentiability of typical Lipschitz functions
The main result of the paper is: If \(E\) is an analytic subset of \([0, 1]\), then the following statements are equivalent: (i) The set of those functions \(f\in \text{Lip}_1\) which are differentiable at no point of \(E\) is residual in \(\text{Lip}_1\) (where \(\text{Lip}_1= \{f: [0, 1]\to \mathbb{R}, |f(y)- f(x)|\leq |x- y|, \forall x, y\in [0, 1]\}\) is endowed with the topology of the uniform convergence). (ii) The set \(E\) is contained in an \(F_\sigma\) subset of \([0, 1]\) of measure zero.
scientific article; zbMATH DE number 756667