Measurable equidecompositions for group actions with an expansion property

Łukasz Grabowski, András Máthé, Oleg Pikhurko

Given an action of a group $\Gamma$ on a measure space $\Omega$, we provide a sufficient criterion under which two sets $A,B\subseteq \Omega$ are measurably equidecomposable, i.e., $A$ can be pa…