On d-bar-approachability, entropy density and B-free shifts
Résumé
We study approximation schemes for shift spaces over a finite alphabet using (pseudo)metrics connected to Ornstein's d metric. This leads to a class of shift spaces we call d-approachable. A shift space d-approachable when its canonical sequence of Markov approximations converges to it also in the d sense. We give a topological characterisation of chain mixing d-approachable shift spaces. As an application we provide a new criterion for entropy density of ergodic measures. Entropy-density of a shift space means that every invariant measure µ of such a shift space is the weak * limit of a sequence µn of ergodic measures with the corresponding sequence of entropies h(µn) converging to h(µ). We prove ergodic measures are entropy-dense for every shift space that can be approximated in the d
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