Superdensity with respect to Radon measure on ${\mathbf{R}}^n$

We introduce and investigate superdensity and the density degree of sets with respect to a Radon measure on ${\mathbf{R}}^n$. Some applications are provided. In particular we prove a result on the approximability of a set by closed subsets of small density degree and a generalization of Schwarz’s theorem on cross derivatives.