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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Measures invariant under local homeomorphisms


Author: David Ross
Journal: Proc. Amer. Math. Soc. 102 (1988), 901-905
MSC: Primary 28C10; Secondary 03H05, 28E05
MathSciNet review: 934864
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Abstract: Suppose $ X$ is a compact Hausdorff space, and $ G$ is a set of local homeomorphisms of $ X$; sufficient conditions are given for the existence of a $ G$-invariant Borel probability measure $ P$ on $ X$. The result generalizes theorems of Mycielski and Steinlage. The proof is an application of the "Loeb measure" construction from nonstandard analysis.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0934864-4
PII: S 0002-9939(1988)0934864-4
Article copyright: © Copyright 1988 American Mathematical Society