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On a Universal Borel Adic Space

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We prove that the so-called uniadic graph and its adic automorphism are Borel universal, i.e., every aperiodic Borel automorphism is isomorphic to the restriction of this automorphism to a subset invariant under the adic transformation, the isomorphism being defined on a universal (with respect to the measure) set. We develop the concept of basic filtrations and combinatorial definiteness of automorphisms suggested in our previous paper.

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Authors and Affiliations

  1. St. Petersburg Department of Steklov Institute of Mathematics and St. Petersburg State University, St. Petersburg, Russia

    A. M. Vershik

  2. St. Petersburg State University and St. Petersburg Department of Steklov Institute of Mathematics, St. Petersburg, Russia

    P. B. Zatitskii

Authors
  1. A. M. Vershik
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  2. P. B. Zatitskii
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Correspondence to A. M. Vershik.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 468, 2018, pp. 24–38.

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Vershik, A.M., Zatitskii, P.B. On a Universal Borel Adic Space. J Math Sci 240, 515–524 (2019). https://doi.org/10.1007/s10958-019-04369-9

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  • DOI: https://doi.org/10.1007/s10958-019-04369-9

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