A ratio ergodic theorem for multiparameter non-singular actions
A ratio ergodic theorem for multiparameter non-singular actions
We prove a ratio ergodic theorem for non-singular free ℤ^d and ℝ^d actions, along balls in an arbitrary norm. Using a Chacon–Ornstein type lemma the proof is reduced to a statement about the amount of mass of a probability measure that can concentrate on (thickened) boundaries of balls in ℝ^d …