An extension of Minkowski's singular function
The authors introduce a family of continuous strictly increasing singular (Cantor type) functions \(g_\lambda :[0,1]\rightarrow [0,1]\), \(\lambda \in (0,1)\). The Hausdorff dimension of the set of points where \(g_\lambda \) has a nonvanishing derivative is computed. For \(\lambda =1/2\) one obtains the Minkowski's singular function studied by J.R. Kinney.
scientific article; zbMATH DE number 828422