  Ein, Lazarsfeld and Smith asked whether `equality' holds between two Samuel
type asymptotic multiplicities for a graded system of zero-dimensional ideals
on a smooth complex variety. We find a connection of this question to complex
analysis by showing that the `equality' is equivalent to a particular case of
Demailly's strong continuity property on the convergence of residual
Monge-Amp\`ere masses under approximation of plurisubharmonic functions. On the
other hand, in an appendix of this paper, S\'ebastien Boucksom gives an
algebraic proof of the `equality' in general, using the intersection theory of
b-divisors. We then use these to show that Demailly's strong continuity holds
for a new important class of plurisubharmonic functions.
