On a universal Borel adic space

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.

arXiv comment10 pp, Ref 15

References in corpus (2)

• On the interplay between measurable and topological dynamics
• Universal adic approximation, invariant measures and scaled entropy