ME embeddings for groups
Seminar Room 1, Newton Institute
Two countable discrete groups $G$ and $H$ are said to be measure equivalent, or ME in short, if there is a standard measure space which carries commuting measure-preserving actions of $G$ and $H$ such that each of actions has a fundamental domain of finite measure. For example lattices of a locally compact group are ME to each other. The notion of measure equivalence is introduced by Gromov as a younger brother of quasi-isometry for groups. I will give a survey on ME embeddings.