Measure equivalence of two countable groups means that they admit commuting free measure-preserving group actions
on a common nonzero standard 
-finite measure space,
each with a measurable fundamental domain of
finite positive measure (Furman 1999). It is a measured counterpart of coarse geometric
comparison of groups.
Gaboriau et al. (2026) proved that all Baumslag-Solitar groups 
with 
and 
are measure equivalent, completing the three-class classification of that family.
