The Peano curve and \(\mathcal I\)-approximate differentiability
The main result of the paper says that the first coordinate function of the classical Peano area-filling curve is \({\mathcal I}\)-density and deep \({\mathcal I}\)-density continuous and nowhere \({\mathcal I}\)-approximately differentiable. The paper includes also an example of a bounded \({\mathcal I}\)-approximately continuous function which is not a derivative.
deep \({\mathcal I}\)- density continuous
nowhere \({\mathcal I}\)-approximately differentiable
scientific article; zbMATH DE number 68379