  We prove a large deviation principle for the sequence of push-forwards of
empirical measures in the setting of Riesz potential interactions on compact
subsets K in R^d with continuous external fields. Our results are valid for
base measures on K satisfying a strong Bernstein-Markov type property for Riesz
potentials. Furthermore, we give sufficient conditions on K (which are
satisfied if K is a smooth submanifold) so that a measure on K which satisfies
a mass-density condition will also satisfy this strong Bernstein-Markov
property.
