Corpus ID: 119308368

The Shannon-McMillan-Breiman theorem beyond amenable groups

@article{Nevo2017TheST,
  title={The Shannon-McMillan-Breiman theorem beyond amenable groups},
  author={Amos Nevo and Felix Pogorzelski},
  journal={arXiv: Dynamical Systems},
  year={2017}
}
We introduce a new isomorphism-invariant notion of entropy for measure preserving actions of arbitrary countable groups on probability spaces, which we call orbital Rokhlin entropy. It employs Danilenko's orbital approach to entropy of a partition, and is motivated by Seward's recent generalization of Rokhlin entropy from amenable to general groups. A key ingredient in our approach is the use of an auxiliary probability-measure-preserving hyperfinite equivalence relation. Under the assumption… Expand

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