  We consider OPRL and OPUC with measures regular in the sense of
Ullman-Stahl-Totik and prove consequences on the Jacobi parameters or
Verblunsky coefficients. For example, regularity on $[-2,2]$ implies
$\lim_{N\to\infty} N^{-1} [\sum_{n=1}^N (a_n-1)^2 + b_n^2] =0$.
