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In this paper universality limits are studied in connection with measureswhich exhibit power-type singular behavior somewhere in their support. Weextend the results of Lubinsky for Jacobi measures supported on $ [-1,1] $ togeneralized 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 thesupport. The analysis is based upon the Riemann-Hilbert method, Christoffelfunctions, the polynomial inverse image method of Totik and the normal familyapproach of Lubinsky.

Universality limits for generalized Jacobi measures