  In the class of Ornstein transformations the mixing property satisfies a 0-1
law. Here we consider Ornstein's construction with bounded cutting parameter.
In fact, these latter transformations are not mixing, however it is proved that
the weak mixing property occurs with probability one. Our situation is similar
to the case of interval exchange transformations whose link with the cutting
and stacking construction relies in a dynamical process called Rauzy induction.
