Probabilistic formulation of classical mechanics

Starting axiomatically with a system of finite degrees of freedom whose logic_c is an atomic Boolean -algebra, we prove the existence of phase space_c, as a separable metric space, and a natural (weak) topology on the set of statesI (all the probability measures on_c) such that_c, the subspace of pure statesP, the set of atoms of_c and the spaceP(_c) of all the atomic measures on _c, are all homeomorphic. The only physically accessible states are the points of_c. This probabilistic formulation is shown to be reducible to a purely deterministic theory.