Abstract
It is proved that if a metric space is subjected to a mixing transformation, then there exists a positive numberx 0 such that the probability that any arbitrary set of positive measure is asymptotically mapped into a set of diameter less thanx 0 is zero. Physical implications of this result, in particular the interpretation of Poincaré recurrence, are discussed.
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Erber, T., Schweizer, B. & Sklar, A. Mixing transformations on metric spaces. Commun.Math. Phys. 29, 311–317 (1973). https://doi.org/10.1007/BF01646133
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DOI: https://doi.org/10.1007/BF01646133