Abstract
In the case of r n -adic filtrations, Vershik’s standardness criterion takes a particular form, hereafter called Vershik’s intermediate level criterion. This criterion, whose nature is combinatorial, has been intensively used in the ergodic-theoretic literature, but it is not easily applicable by probabilists because it is stated in a language specific to the theory of measurable partitions and has not been translated into probabilistic terms. We aim to provide an easily applicable probabilistic statement of this criterion. Finally, Vershik’s intermediate level criterion is illustrated by revisiting Vershik’s definition of the scale of an invertible measure-preserving transformation.
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Acknowledgements
I thank Michel Émery and Anatoly Vershik for the interest they have expressed in this work, and I also thank Michel Émery for helpful comments on a previous version of the paper.
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Laurent, S. (2013). Vershik’s Intermediate Level Standardness Criterion and the Scale of an Automorphism. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLV. Lecture Notes in Mathematics(), vol 2078. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00321-4_3
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DOI: https://doi.org/10.1007/978-3-319-00321-4_3
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