Summary
Let α be a coding: B→A, to which is associated a mapping \(Q \to Q^\alpha\)from the set of ergodic measures on B ℤ to the set of ergodic measures on A ℤ. We derive a relation between the number of ergodic solutions of the equation \(P = Q^\alpha\)where P is a given ergodic measure on A ℤ, and the ambiguousness of decoding for each of the solutions Q.
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Laboratoire de Probabilités, tour 46–56, 3 ème étage, 4, Place Jussieu, F-75230 Paris Cedex 05. Laboratoire associé au CNRS n°224 «Processus Stochastiques et Applications»
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Blanchard, F., Perrin, D. Relèvement d'une mesure ergodique par un codage. Z. Wahrscheinlichkeitstheorie verw Gebiete 54, 303–311 (1980). https://doi.org/10.1007/BF00534348
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DOI: https://doi.org/10.1007/BF00534348