Measurable equidecompositions for group actions with an expansion property
Łukasz GrabowskiLancaster University, UK
András MáthéUniversity of Warwick, Coventry, UK
Oleg PikhurkoUniversity of Warwick, Coventry, UK
Given an action of a group on a measure space , we provide a sufficient criterion under which two sets are , i.e., can be partitioned into finitely many measurable pieces which can be rearranged using some elements of to form a partition of . In particular, we prove that every bounded measurable subset of , , with non-empty interior is measurably equidecomposable to a ball via isometries. The analogous result also holds for some other spaces, such as the sphere or the hyperbolic space of dimension .
Cite this article
Łukasz Grabowski, András Máthé, Oleg Pikhurko, Measurable equidecompositions for group actions with an expansion property. J. Eur. Math. Soc. 24 (2022), no. 12, pp. 4277–4326DOI 10.4171/JEMS/1189