  Given a Bratteli diagram D we consider the compact topological space formed
by all infinite paths on D. Two such path are said to be tail-equivalent when
they "have the same tail", i.e. when they eventually coincide. This equivalence
relation is approximately proper and hence one may consider the C*-algebra
associated to it according to a procedure recently introduced by the first
named author and A. Lopes. The main result of this work is the proof that this
algebra is isomorphic to the AF-algebra associated to the given Bratteli
diagram.
