Von Neumann and Birkhoff ergodic theorems for negatively curved groups
Von Neumann and Birkhoff ergodic theorems for negatively curved groups
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 …