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.
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Anders Johansson, Anders Öberg, Mark Pollicott, Unique Bernoulli -measures. J. Eur. Math. Soc. 14 (2012), no. 5, pp. 1599–1615DOI 10.4171/JEMS/342