Extensions of Lattice Set Functions to Regular Borel Measures

Abstract

This paper deals with the unique extension of a finite regular set function from the $\delta$-lattice of all compact $G_\delta$-subsets of a locally compact Hausdorff space to a finite regular measure on the $\delta$-ring of all relatively compact Borel subsets of the space. This extension is a two-step method because it is performed (without density assumptions) via the $\delta$-ring of all relatively compact Baire subsets of the space.