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
Canonical name	VitaliCovering
Date of creation	2013-03-22 13:29:48
Last modified on	2013-03-22 13:29:48
Owner	Koro (127)
Last modified by	Koro (127)
Numerical id	6
Author	Koro (127)
Entry type	Definition
Classification	msc 54E99
Defines	Vitali class