Borel measure extensions of measures defined on sub-sigma-algebras

摘要

We develop a new approach to the measure extension problem, based on nonstandard analysis, The class of thick topological spaces. which includes all locally compact and all K-analytic spaces, is introduced in this paper, and measure extension results of the following type lire obtained: If (X, T) is a regular, Lindelof, and thick space, A subset of sigma[T] is a sigma-algebra, and nu is a finite measure A, inner regular with respect to the closed sets in A, then nu has a Radon extension. The methods developed here allow us to improve on previously known extension results. (C) 2000 Academic Press. [References: 37]