On the property \(N^{- 1}\)
Summary: We construct a continuous function \(f : [0,1] \rightarrow \mathbb{R}\) such that \(f\) possesses \(N^{- 1}\)-property, but \(f\) does not have approximate derivative on a set of full Lebesgue measure. This shows that Banach's Theorem concerning differentiability of continuous functions with Lusin's property \((N)\) does not hold for \(N^{- 1}\)-property. Some relevant properties are presented.
scientific article; zbMATH DE number 6929339