# Vitali covering

A collection of sets $\mathscr{V}$ in a metric space $X$ is called a Vitali covering (or Vitali class) for $X$ if for each $x\in X$ and $\delta>0$ there exists $U\in\mathscr{V}$ such that $x\in U$ and $0<\operatorname{diam}(U)\leq\delta$.

Title Vitali covering VitaliCovering 2013-03-22 13:29:48 2013-03-22 13:29:48 Koro (127) Koro (127) 6 Koro (127) Definition msc 54E99 Vitali class