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

DOI:
https://doi.org/10.1090/S0002-9947-1984-0752507-0

MathSciNet review:
752507

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Abstract: Let be a compact Riemannian manifold with covering space , and suppose is a family of Borel probability measures on , all of which arise from some fixed measure by -homotheties of about some point, followed by renormalization of the resulting measure. In this paper we study the ergodic properties, as a function of , of the corresponding family of projected measures on 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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DOI:
https://doi.org/10.1090/S0002-9947-1984-0752507-0

Article copyright:
© Copyright 1984
American Mathematical Society