Asymptotic multiplicities and Monge-Ampere masses (with an appendix by Sebastien Boucksom)

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-Ampere masses under approximation of plurisubharmonic functions. On the other hand, in an appendix of this paper, Sebastien 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.