Measurable Hall's theorem for actions of abelian groups
Logic
2021-07-08 v2 Combinatorics
Metric Geometry
Abstract
We prove a measurable version of the Hall marriage theorem for actions of finitely generated abelian groups. In particular, it implies that for free measure-preserving actions of such groups, if two equidistributed measurable sets are equidecomposable, then they are equidecomposable using measurable pieces. The latter generalizes a recent result of Grabowski, M\'ath\'e and Pikhurko on the measurable circle squaring and confirms a special case of a conjecture of Gardner.
Keywords
Cite
@article{arxiv.1903.02987,
title = {Measurable Hall's theorem for actions of abelian groups},
author = {Tomasz Cieśla and Marcin Sabok},
journal= {arXiv preprint arXiv:1903.02987},
year = {2021}
}