We study the equivalence of microcanonical and canonical ensembles in continuous systems, in the sense of the convergence of the corresponding Gibbs measures. This is obtained by proving a local central limit theorem and a local large deviations principle. As an application we prove a formula due to Lebowitz-Percus-Verlet. It gives mean square fluctuations of an extensive observable, like the kinetic energy, in a classical micro canonical ensemble at fixed energy.