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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Compact measures have Loeb preimages


Author: David Ross
Journal: Proc. Amer. Math. Soc. 115 (1992), 365-370
MSC: Primary 28E05; Secondary 03H05, 28C99, 60B99
MathSciNet review: 1079898
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Abstract: A compact measure is a (possibly nontopological) measure that is inner-regular with respect to a compact family of measurable sets. The main result of this paper is that every compact probability measure is the image, under a measure-preserving transformation, of a Loeb probability space. This generalizes a well-known result about Radon topological probability measures. It is also proved that a compact probability space can be topologized in such a way that the measure is essentially Radon.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1079898-8
Keywords: Loeb measure, compact measure, Radon measure
Article copyright: © Copyright 1992 American Mathematical Society