  Consider an invertible measure-preserving transformation of a probability
space. A finite partition of the space is called weakly independent if there
are infinitely many images of this partition under powers of the transformation
that are jointly independent. Krengel proved that a transformation is weakly
mixing if and only if weakly independent partitions of the underlying space are
dense among all finite partitions. Using the tools developed in the later
papers of del Junco-Reinhold-Weiss and del Junco-Begun we obtain Krengel- type
results for weakly mixing random dynamical systems (or equivalently, skew
products that are relatively weakly mixing).
