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The ergodic theorem for additive cocycles of ℤd or ℝd

Published online by Cambridge University Press:  19 September 2008

Daniel Boivin and
Yves Derriennic
Daniel Boivin
Affiliation:
The Ohio State University, Columbus, Ohio 43210, USA
Yves Derriennic
Affiliation:
Université de Bretagne Occidentale, Brest, France
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Extract

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 ℤd or ℝd (d ≥ 1), acts on Ω by measure-preserving transformations. This action is denned by a map

which is jointly measurable, such that Tx+y = TxTy and Txμ = μ

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 1 , March 1991, pp. 19 - 39
Copyright
Copyright © Cambridge University Press 1991

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References

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