Gibbs random fields invariant under infinite-particle Hamiltonian dinamics

The Liouville operator for an infinite-particle Hamiltoniaa dynamics corresponding to interaction potential $U$ is used to introduce the concept of a locally weakly invariant measure on the phase space and to show that if a Gibbs measure with potential of general form is locally weakly invariant then its Hamiltonian is asymptotically an additive integral of the motion of the particles with the interaction $U$.