  For Hoelder cocycles over a Lipschitz base transformation, possibly
non-invertible, we show that the subbundles given by the Oseledets Theorem are
Hoelder-continuous on compact sets of measure arbitrarily close to 1. The
results extend to vector bundle automorphisms, as well as to the
Kontsevich-Zorich cocycle over the Teichmueller flow on the moduli space of
abelian differentials. Following a recent result of Chaika-Eskin, our results
also extend to any given Teichmueller disk.
