  We point out an example of a projective family $\pi : X \to S$, a
$\pi$-pseudoeffective divisor $D$ on $X$, and a subvariety $V \subset X$ for
which the asymptotic multiplicity $\sigma_V(D;X/S)$ is infinite. This shows
that the divisorial Zariski decomposition is not always defined for
pseudoeffective divisors in the relative setting.
