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arXiv · 1303.4109

von-Neumann and Birkhoff ergodic theorems for negatively curved groups

Lewis Bowen·Amos Nevo
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Abstract

We prove maximal inequalities for concentric ball and spherical shell averages on a general Gromov hyperbolic group, in arbitrary probability preserving actions of the group. Under an additional condition, satisfied for example by all groups acting isometrically and properly discontinuously on CAT(-1) spaces, we prove a pointwise ergodic theorem with respect to a sequence of probability measures supported on concentric spherical shells.

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Lewis Bowen, Amos Nevo. 2013-03-17. von-Neumann and Birkhoff ergodic theorems for negatively curved groups. https://arxiv.org/abs/1303.4109

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