Groups, Geometry, and Dynamics


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Volume 8, Issue 2, 2014, pp. 331–353
DOI: 10.4171/GGD/228

Published online: 2014-07-08

A horospherical ratio ergodic theorem for actions of free groups

Lewis Bowen[1] and Amos Nevo[2]

(1) The University of Texas at Austin, USA
(2) Technion - Israel Institute of Technology, Haifa, Israel

We prove a ratio ergodic theorem for discrete non-singular measurable equivalence relations, provided they satisfy a strong form of the Besicovich covering property. In particular, this includes all hyperfinite measurable equivalence relation. We then use this result to study general non-singular actions of non-abelian free groups and establish a ratio ergodic theorem for averages along horospheres.

Keywords: Ratio ergodic theorem, free groups

Bowen Lewis, Nevo Amos: A horospherical ratio ergodic theorem for actions of free groups. Groups Geom. Dyn. 8 (2014), 331-353. doi: 10.4171/GGD/228