  It is shown by constructing Rohlins canonical measures that for a strictly
stationary, d-dimensional vector-valued process X there exists another strictly
stationary d-dimensional process U with uniform one-dimensional marginals and
with the same mixing properties as X, such that X is a finitary factor of U of
coding length 1, and such that the projection map is order preserving in each
coordinate. As an application this extends the a.s. approximation of the
empirical distribution function of weakly dependent random vectors with
continuous distribution function in [1] and [3] to the general case.
