  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.
