## Compact measures have Loeb preimages

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- by David Ross
- Proc. Amer. Math. Soc.
**115**(1992), 365-370 - DOI: https://doi.org/10.1090/S0002-9939-1992-1079898-8
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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.## References

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## Bibliographic Information

- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**115**(1992), 365-370 - MSC: Primary 28E05; Secondary 03H05, 28C99, 60B99
- DOI: https://doi.org/10.1090/S0002-9939-1992-1079898-8
- MathSciNet review: 1079898