We study the measurable dynamical properties of the interval map
generated by the model-case erasing substitution $\rho$, defined by:
$ \rho(00) = empty word$; ?$\rho(01) = 1$; $\rho?(10) = 0$; $\rho(11) = 01$.
We prove that, although the map is singular, its square preserves the
Lebesgue measure and is strongly mixing, thus ergodic, with respect to
it. We discuss the extension of the results to more general erasing maps.
KEYWORDS: Mixing; Substitutions; Combinatorics on Words.