Measures invariant under local homeomorphisms

Ross, David

doi:10.1090/S0002-9939-1988-0934864-4

Measures invariant under local homeomorphisms
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Proc. Amer. Math. Soc. 102 (1988), 901-905 Request permission

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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Measurable transformations and saturated models of analysis

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