  It is well known that the composition operator on Hardy or Bergman space has
a closed range if and only if its Navanlinna counting function induces a
reverse Carleson measure. Similar conclusion is not available on the Dirichlet
space. Specifically, the reverse Carleson measure is not enough to ensure that
the range of the corresponding composition operator is closed. However, under
certain assumptions, we in this paper set the necessary and sufficient
condition for a composition operator on the Dirichlet space to have closed
range.
