  Let $M$ be a closed oriented $C^\infty$ manifold and $f$ a $C^\infty$ Anosov
diffeomorphism on $M$. We show that if $M$ is the two torus $T^2$, then $f$ is
conjugate to a hyperbolic automorphism of $T^2$, either by a $C^\infty$
diffeomorphism or by a singular homeomorphism. We also show that for general
$M$, if $f$ admits an absolutely continuous invariant measure $\mu$, then $\mu$
is a $C^\infty$ volume. The proofs are concatenations of well known results in
the field.
