Hokkaido Mathematical Journal

MATSUMOTO Shigenori,

The unique ergodicity of equicontinuous laminations.

Hokkaido Mathematical Journal, 39 (2010) pp.389-403

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Abstract

We prove that a transversely equicontinuous minimal lamination on a locally compact metric space $Z$ has a transversely invariant nontrivial Radon measure. Moreover if the space $Z$ is compact, then the tranversely invariant Radon measure is shown to be unique up to a scaling.

MSC(Primary)53C12
MSC(Secondary)37C85
Uncontrolled Keywordslamination, foliation, transversely invariant measure, unique ergodicity