Measurable Hall's theorem for actions of abelian groups
- Speaker(s)
- Tomasz Cieśla
- Affiliation
- McGill University
- Date
- May 22, 2019, 4:15 p.m.
- Room
- room 5050
- Seminar
- Topology and Set Theory Seminar
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, Máthé and Pikhurko on the measurable
circle squaring and confirms a special case of a conjecture of
Gardner. This is joint work with Marcin Sabok.