  We show that the set of Bernoulli measures of an isolated topologically
mixing homoclinic class of a generic diffeomorphism is a dense subset of the
set of invariant measures supported on the class. For this, we introduce the
large periods property and show that this is a robust property for these
classes. We also show that the whole manifold is a homoclinic class for an open
and dense subset of the set of robustly transitive diffeomorphisms far away
from homoclinic tangencies. In particular, using results from Abdenur and
Crovisier, we obtain that every diffeomorphism in this subset is robustly
topologically mixing.
