JournalsggdVol. 8, No. 2pp. 331–353

A horospherical ratio ergodic theorem for actions of free groups

  • Lewis Bowen

    The University of Texas at Austin, USA
  • Amos Nevo

    Technion - Israel Institute of Technology, Haifa, Israel
A horospherical ratio ergodic theorem for actions of free groups cover
Download PDF

Abstract

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.

Cite this article

Lewis Bowen, Amos Nevo, A horospherical ratio ergodic theorem for actions of free groups. Groups Geom. Dyn. 8 (2014), no. 2, pp. 331–353

DOI 10.4171/GGD/228