Unbalancedness of the conjugacy relation of ergodic measure-preserving transformations
Bo Peng
公開日: 2025/10/6
Abstract
We show that the isomorphism of ergodic measure-preserving transformations is not Borel reducible to the relation induced by the conjugacy action of the full group of an ergodic measure-preserving transformation on itself. This answers a question of Le Ma\^{i}tre in the negative and gives a positive indication towards a conjecture of Sabok. In fact, we prove that the isomorphism of ergodic measure-preserving transformation is unbalanced, which answers another question of Le Ma\^{i}tre in the positive.