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Totally Ergodic Generalised Matrix Equilibrium States have the Bernoulli Property
Abstract We show that every totally ergodic generalised matrix equilibrium state is $$\psi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ψ</mml:mi> </mml:math> -mixing with respect to the natural partition into cylinders and hence is measurably isomorphic to a Bernoulli shift in its natural extension. This implies that the natural extensions of ergodic generalised matrix …