A pathology of asymptotic multiplicity in the relative setting

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