  In this paper we continue the study, started in [1], of the operatorial
formulation of classical mechanics given by Koopman and von Neumann (KvN) in
the Thirties. In particular we show that the introduction of the KvN Hilbert
space of complex and square integrable "wave functions" requires an enlargement
of the set of the observables of ordinary classical mechanics. The possible
role and the meaning of these extra observables is briefly indicated in this
work. We also analyze the similarities and differences between non selective
measurements and two-slit experiments in classical and quantum mechanics.
