  A formalism is developed for describing approximate classical behaviour in
finite (but possibly large) quantum systems. This is done in terms of a
structure common to classical and quantum mechanics, viz. a Poisson space with
a transition probability. Both the limit where Planck's constant goes to zero
in a fixed finite system and the limit where the size of the system goes to
infinity are incorporated. In either case, classical behaviour is seen only for
certain observables and in a restricted class of states.
