  Brolin-Lyubich measure $\lambda_R$ of a rational endomorphism
$R:\riem\to\riem$ with $\deg R\geq 2$ is the unique invariant measure of
maximal entropy $h_{\lambda_R}=h_{\text{top}}(R)=\log d$. Its support is the
Julia set $J(R)$. We demonstrate that $\lambda_R$ is always computable by an
algorithm which has access to coefficients of $R$, even when $J(R)$ is not
computable. In the case when $R$ is a polynomial, Brolin-Lyubich measure
coincides with the harmonic measure of the basin of infinity. We find a
sufficient condition for computability of the harmonic measure of a domain,
which holds for the basin of infinity of a polynomial mapping, and show that
computability may fail for a general domain.
