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Bernoulli shifts and local density property

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Abstract

We consider the property LocDen for the squaring mapping into the space of all measure preserving transformations and into the space of mixing transformations. It is proved that Bernoulli shifts with infinite entropy do not possess this property.

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Authors and Affiliations

  1. Chair of High and Applied Mathematics, Russian State University of Trade and Economics, Smol’naya st., 36, Moscow, 125993, Russia

    S. V. Tikhonov

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  1. S. V. Tikhonov
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Additional information

Original Russian Text © S.V. Tikhonov, 2012, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2012, Vol. 67, No. 1, pp. 31–37.

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Tikhonov, S.V. Bernoulli shifts and local density property. Moscow Univ. Math. Bull. 67, 29–35 (2012). https://doi.org/10.3103/S0027132212010056

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  • DOI: https://doi.org/10.3103/S0027132212010056

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