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.
Classification :
37-XX
Mots-clés :
Ratio ergodic theorem, free groups
Affiliations des auteurs :
Lewis Bowen
1
;
Amos Nevo
2
1
The University of Texas at Austin, USA
2
Technion - Israel Institute of Technology, Haifa, Israel
Lewis Bowen; Amos Nevo. A horospherical ratio ergodic theorem for actions of free groups. Groups, geometry, and dynamics, Tome 8 (2014) no. 2, pp. 331-353. doi: 10.4171/ggd/228
@article{10_4171_ggd_228,
author = {Lewis Bowen and Amos Nevo},
title = {A horospherical ratio ergodic theorem for actions of free groups},
journal = {Groups, geometry, and dynamics},
pages = {331--353},
year = {2014},
volume = {8},
number = {2},
doi = {10.4171/ggd/228},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/228/}
}
TY - JOUR
AU - Lewis Bowen
AU - Amos Nevo
TI - A horospherical ratio ergodic theorem for actions of free groups
JO - Groups, geometry, and dynamics
PY - 2014
SP - 331
EP - 353
VL - 8
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/228/
DO - 10.4171/ggd/228
ID - 10_4171_ggd_228
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%J Groups, geometry, and dynamics
%D 2014
%P 331-353
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%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/228/
%R 10.4171/ggd/228
%F 10_4171_ggd_228
