  In this paper universality limits are studied in connection with measures
which exhibit power-type singular behavior somewhere in their support. We
extend the results of Lubinsky for Jacobi measures supported on $ [-1,1] $ to
generalized Jacobi measures supported on a compact subset of the real line,
where the singularity can be located in the interior or at an endpoint of the
support. The analysis is based upon the Riemann-Hilbert method, Christoffel
functions, the polynomial inverse image method of Totik and the normal family
approach of Lubinsky.
