Unique Bernoulli -measures

  • Anders Johansson

    University of Gävle, Sweden
  • Anders Öberg

    Uppsala University, Sweden
  • Mark Pollicott

    University of Warwick, Coventry, UK


We improve and subsume the conditions of Johansson and Öberg and Berbee for uniqueness of a -measure, i.e., a stationary distribution for chains with complete connections. In addition, we prove that these unique -measures have Bernoulli natural extensions. We also conclude that we have convergence in the Wasserstein metric of the iterates of the adjoint transfer operator to the -measure.

Cite this article

Anders Johansson, Anders Öberg, Mark Pollicott, Unique Bernoulli -measures. J. Eur. Math. Soc. 14 (2012), no. 5, pp. 1599–1615

DOI 10.4171/JEMS/342