Analytical approximations and Monge-Amp\`{e}re masses of plurisubharmonic singularities

We construct examples of plurisubharmonic functions with isolated singularities at $0\in {\mathbb{C}}^n$, whose residual Monge-Amp`{e}re masses at the origin can not be approximated by masses of analytic approximations obtained via multiplier ideals. This answers negatively a conjecture of Demailly.