The dimension of a closed subset of \(\mathbb{R}^ n\) and related function spaces
Two notions of the dimension of a non-empty closed subset \(F\) of \(\mathbb{R}^n\) with empty interior are introduced. The first is connected with the question of whether, in some Besov function space, there exists a non-trivial singular distribution with support on \(F\). The second is related to \(\varepsilon\)-entropy and \(\varepsilon\)-capacity of \(F\) and its neighbourhood and is connected with atomic representation of function spaces. New Besov function spaces are introduced.
scientific article; zbMATH DE number 794422
scientific article