  Let $G$ be a residually finite group.
  We give an explicit example in the discrete Heisenberg group that the Brown
measure of multiplication operators
  $A \in \mathbb{Z}[G] \subseteq \mathcal{B}(\ell^2(G))$
  in general can not be approximated using finite quotients $G/N$ of $G$.
  We show that in finitely generated abelian groups the Brown measure can be
approximated using finite quotients.
