  We show that for any $C^1$ partially hyperbolic diffeomorphism, there is a
full volume subset, such that any Cesaro limit of any point in this subset
satisfies the Pesin formula for partial entropy.
  This result has several important applications. First we show that for any
$C^{1+}$ partially hyperbolic diffeomorphism with one dimensional center, there
is a full volume subset, such that every point in this set belongs to either
the basin of a physical measure with non-vanishing center exponent, or the
center exponent of any limit of the sequence
$\frac1n\sum_{i=0}^{n-1}\delta_{f^i(x)}$ is vanishing.
  We also prove that for any diffeomorphism with mostly contracting center, it
admits a $C^1$ neighborhood such that every diffeomorphism in a $C^1$ residual
subset of this open set admits finitely many physical measure, whose basins
have full volume.
