On the convergence in capacity of rational approximants

Let {r(n)} be a sequence of rational functions (deg r(n) less than or equal to n) that converge rapidly in measure to an analytic function f on an open set in C-N. We show that {r(n)} converges rapidly in capacity to f on its natural domain of definition W-f (which, by a result of Goncar, is an open subset of C-N). In particular, for f meromorphic on CN and analytic near zero the sequence of Pade approximants {pi (n),(z, f, lambda)} (as defined by Goncar) converges rapidly in capacity to f on C-N.