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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The behavior under projection of dilating sets in a covering space


Author: Burton Randol
Journal: Trans. Amer. Math. Soc. 285 (1984), 855-859
MSC: Primary 58C35; Secondary 28D99
MathSciNet review: 752507
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Abstract: Let $ M$ be a compact Riemannian manifold with covering space $ S$, and suppose $ d{\mu_r}\;(0 < r < \infty )$ is a family of Borel probability measures on $ S$, all of which arise from some fixed measure by $ r$-homotheties of $ S$ about some point, followed by renormalization of the resulting measure. In this paper we study the ergodic properties, as a function of $ r$, of the corresponding family of projected measures on $ M$ in the Euclidean and hyperbolic cases. A typical example arises by considering the behavior of a dilating family of spheres under projection.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0752507-0
PII: S 0002-9947(1984)0752507-0
Article copyright: © Copyright 1984 American Mathematical Society