Convergent interpolatory quadrature rules and orthogonal polynomials of varying measures

Let (P-n) be a sequence of polynomials such that P-n(x) >0 for x [-1, 1] and in}{-69pt} , where is a measure on [-1, 1] that is regular in the sense of Stahl and Totik. We prove that the interpolatory quadrature rule with nodes at the zeros of q(n) is convergent with respect to provided that the zeros of P-n lie outside a certain curve surrounding [-1, 1].