  We show that for a given finitely generated group, its Bernoulli shift space
can be equivariantly embedded as a subset of a space of pointed trees with
Gromov-Hausdorff metric and natural partial action of a free group. Since the
latter can be realised as a transverse space of a foliated space with leaves
Riemannian manifolds, this embedding allows us to obtain a suspension of such
Bernoulli shift. By a similar argument we show that the space of pointed trees
is universal for compactly generated expansive pseudogroups of transformations.
