Topological vitali measure spaces

Abstract

The properties of Lebesgue outer measures embodied in the Vitali covering theorem, the Vitali-Carathéodory theorem, the Lusin theorem, the density theorem, outer regularity and inner regularity, and the relation between measurability and approximate continuity are studied in a general abstract space, called a topological Vitali measure space. The main theme is the mutual equivalence of these properties.