  We address the classical problem of equivalence between Kolmogorov and
Bernoulli property of smooth dynamical systems. In a natural class of volume
preserving partially hyperbolic diffeomorphisms homotopic to Anosov ("derived
from Anosov") on 3-torus, we prove that Kolmogorov and Bernoulli properties are
equivalent.
  In our approach, we propose to study the conditional measures of volume along
central foliation to recover fine ergodic properties for partially hyperbolic
diffeomorphisms. As an important consequence we obtain that there exists an
almost everywhere conjugacy between any volume preserving derived from Anosov
diffeomorphism of 3-torus and its linearization.
  Our results also hold in higher dimensional case when central bundle is one
dimensional and stable and unstable foliations are quasi-isometric.
