The ergodic theorem for additive cocycles of ℤ d or ℝ d

1991/03/01 by Daniel Boivin, Yves Derriennic

paper · doi:10.1017/s014338570000599x

Abstract

Let us consider (Ω, , μ, G ) a measure-preserving dynamical system, (Ω, , μ) is a probability space. The group G , which is supposed to be either ℤ d or ℝ d ( d ≥ 1), acts on Ω by measure-preserving transformations. This action is denned by a map which is jointly measurable, such that T x + y = T x T y and T x μ = μ

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