Hausdorff dimension and countable Borel equivalence relations

Andrew Marks, Dino Rossegger, Theodore Slaman

We show that if $E$ is a countable Borel equivalence relation on ${\mathbb{R}}^n$, then there is a closed subset $A\subset [0,1{]}^n$ of Hausdorff dimension $n$ so that $E \restrictio…