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 on a dynamical process called Rauzy induction.

The second author was partially supported by grants from CNPq-Brazil 301456/80 and FINEP/ CNPq/MCT 41.96.0923.00 (PRONEX)