Email this article On a Universal Borel Adic Space
- Authors: Vershik A.M.1, Zatitskii P.B.2
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Affiliations:
- St. Petersburg Department of Steklov Institute of Mathematics and St. Petersburg State University
- St. Petersburg State University and St. Petersburg Department of Steklov Institute of Mathematics
- Issue: Vol 240, No 5 (2019)
- Pages: 515-524
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242776
- DOI: https://doi.org/10.1007/s10958-019-04369-9
- ID: 242776
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Abstract
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.
About the authors
A. M. Vershik
St. Petersburg Department of Steklov Institute of Mathematics and St. Petersburg State University
Author for correspondence.
Email: avershik@pdmi.ras.ru
Russian Federation, St. Petersburg
P. B. Zatitskii
St. Petersburg State University and St. Petersburg Department of Steklov Institute of Mathematics
Email: avershik@pdmi.ras.ru
Russian Federation, St. Petersburg
