Let $M$ be a compact smooth manifold, let $f: M \to M$ be a $C^1$ Axiom A diffeomorphism, and let $\Lambda \subset M$ be a basic set such that the restricted dynamical system
paragraph
admin
\begin{align*}
T: \Lambda \to \Lambda,\quad x \mapsto f(x)
\end{align*}
be the corresponding finite-to-one coding map, so that $\pi \circ \sigma = T \circ \pi$. If $m_A$ denotes the Parry measure of $\sigma: \Sigma_A \to \Sigma_A$, then
paragraph
admin
\begin{align*}
\mu_B := \pi_* m_A
\end{align*}
latex_env
admin
is the unique $T$-invariant Borel probability measure on $\Lambda$ satisfying