Borel Measure Extensions of Measures Defined on Sub-σ-Algebras

Abstract

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 are obtained: If (X, T) is a regular, Lindelöf, and thick space, A⊂σ[T] is a σ-algebra, and ν is a finite measure on A, inner regular with respect to the closed sets in A, then ν has a Radon extension. The methods developed here allow us to improve on previously known extension results.