Limit groups, positive-genus towers and measure equivalence
  By definition, an $\omega$-residually free tower is positive-genus if all surfaces used in its construction are of positive genus. We prove that every limit group is virtually a subgroup of a positive-genus $\omega$-residually free tower. By combining this with results of Gaboriau, we prove that elementarily free groups are measure equivalent to free groups. 
Martin R Bridson, Michael Tweedale, Henry Wilton