  In this paper we establish asymptotic results for Christoffel functions with
respect to measures supported on Jordan curves having a Radon-Nikodym
derivative with a jump singularity. We extend the results known for measures
supported in the interval $ [-1,1] $ to more general sets, for example a system
of Jordan curves, using polynomial inverse images. It is shown that the
asymptotic limit can be written in terms of the equilibrium measure or Green's
function.
