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Group extensions of Gibbs–Markov maps

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Abstract

 Let φ be an aperiodic cocycles with values in a locally compact abelian second countable group ? defined on an exact Gibbs–Markov map T : X → X. We show that the group extension T φ (x,g) = (T(x),g + φ(x)) (x ? X; g ??) is exact. Equivalent conditions for exactness are found.

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Received: 20 April 2000 / Revised version: 25 June 2001 / Published online: 13 May 2002

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Aaronson, J., Denker, M. Group extensions of Gibbs–Markov maps. Probab Theory Relat Fields 123, 28–40 (2002). https://doi.org/10.1007/s004400100173

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Keywords

  • Equivalent Condition
  • Group Extension
  • Countable Group