General expressions are found for the orthonormal polynomials and the
kernels relative to measures on the real line of the form mu + Mdelta(
c), in terms of those of the measures dmu and (x - c)2dmu. In particul
ar, these relations allow us to show that Nevai's class M(0, 1) is clo
sed under adding a mass point, as well as obtain several bounds for th
e polynomials and kernels relative to a generalized Jacobi weight with
a finite number of mass points.