Some aspects of the metric space of pluriregular polynomially convex compact subsets of C^n

In the family of all pluriregular polynomially convex compact subsets of C^n consider the metric associated with the pluricomplex Green functions of the sets. Some properties, comparisons with the Hausdorff metric and few open problems are listed. A special iterated functions system (IFS) in the metric space is considered, its attractor being a Julia type set. A Monte Carlo approximation of such kinds of sets is proposed.