Differentiability and density continuity (Q750637)

The paper deals with the relationship between density continuity and differentiability. Among others it is proved that an arbitrary closed set is a zero set of a \(C^{\infty}\) density continuous function and that there exists a nowhere approximately differentiable density continuous and continuous function. The proofs are based upon earlier results of the authors and a theorem of \textit{J. Malý} [Real Anal. Exch. 5, 326-329 (1980; Zbl 0443.26006)].