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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1992-1079898-8

Keywords:
Loeb measure,
compact measure,
Radon measure

Article copyright:
© Copyright 1992
American Mathematical Society