**Abstract : ** We consider the one-dimensional Cantor set $K$ in the plane also known as the one-quarter Cantor set,
and define an elliptic operator on $R^2 \setminus K$
for which the elliptic measure, with pole at infinity, is exactly proportional to the standard invariant measure $\mu$ on $K$.
The operator has the nice form
$L = div a \nabla$, but with an appropriate scalar function $a$. It was known that for the Laplacian, the harmonic measure and $\mu$
are mutually singular,
and the case of $L$ could have been hard to compute.
But in fact, we can simply construct the Green function so that $L$ has the desired properties.