  We consider a smooth area-preserving Anosov diffeomorphism $f\colon \mathbb
T^2\rightarrow \mathbb T^2$ homotopic to an Anosov automorphism $L$ of $\mathbb
T^2$. It is known that the positive Lyapunov exponent of $f$ with respect to
the normalized Lebesgue measure is less than or equal to the topological
entropy of $L$, which, in addition, is less than or equal to the Lyapunov
exponent of $f$ with respect to the probability measure of maximal entropy.
Moreover, the equalities only occur simultaneously. We show that these are the
only restrictions on these two dynamical invariants.
