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Borel Measure Extensions of Measures Defined on Sub--Algebras

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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, ) is a regular, Lindelöf, and thick space, ⊂[] is a -algebra, and is a finite measure on , inner regular with respect to the closed sets in , then has a Radon extension. The methods developed here allow us to improve on previously known extension results. Copyright 2000 Academic Press.

Keywords: Loeb measures; standard part map

Document Type: Research Article

Affiliations: 1: Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, Madrid, 28049, Spain 2: Fachbereich Mathematik, Universität Duisburg, Lotharstr. 65, Duisburg 1, D-4100, Germany

Publication date: March 1, 2000

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