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.

Original languageEnglish
Pages (from-to)515-524
Number of pages10
JournalJournal of Mathematical Sciences (United States)
Volume240
Issue number5
DOIs
StatePublished - 7 Aug 2019

    Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

ID: 88659554