  We prove that if two transvection-free right-angled Artin groups are measure
equivalent, then they have isomorphic extension graphs. As a consequence, two
right-angled Artin groups with finite outer automorphism groups are measure
equivalent if and only if they are isomorphic. This matches the quasi-isometry
classification.
  However, in contrast with the quasi-isometry question, we observe that no
right-angled Artin group is superrigid for measure equivalence in the strongest
possible sense, for two reasons. First, a right-angled Artin group $G$ is
always measure equivalent to any graph product of infinite countable amenable
groups over the same defining graph. Second, when $G$ is nonabelian, the
automorphism group of the universal cover of the Salvetti complex of $G$ always
contains infinitely generated (non-uniform) lattices.
