  In this article we prove that the co-compactness of the arithmetic lattices
in a connected semisimple real Lie group is preserved if the lattices under
consideration are representation equivalent. This is in the spirit of the
question posed by Gopal Prasad and A. S. Rapinchuk where instead of
representation equivalence, the lattices under consideration are weakly
commensurable Zariski dense subgroups.
