  A long series of previous papers have been devoted to the (one-dimensional)
moment problem with nonnegative rational measure. The rationality assumption is
a complexity constraint motivated by applications where a parameterization of
the solution set in terms of a bounded finite number of parameters is required.
In this paper we provide a complete solution of the multidimensional moment
problem with a complexity constraint also allowing for solutions that require a
singular measure added to the rational, absolutely continuous one. Such
solutions occur on the boundary of a certain convex cone of solutions. In this
paper we provide complete parameterizations of all such solutions. We also
provide errata for a previous paper in this journal coauthored by one of the
authors of the present paper.
