LAUSR

For a graded system of zero-dimensional ideals on a smooth complex variety, Ein, Lazarsfeld and Smith asked whether equality holds between two Samuel type asymptotic multiplicities of the given graded system and of the associated asymptotic multiplier ideals respectively. In terms of complex analysis, we first show that the equality is equivalent to a particular case of Demailly's conjecture on the convergence of residual Monge-Ampere masses under the approximation of plurisubharmonic functions with isolated singularities. This yields an analytic proof of the equality when a Kuronya-Wolfe constant of the graded system of ideals is at most $1$. 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 this to confirm Demailly's conjecture for Green and Siu functions associated to graded systems of ideals and obtain further analytic consequences.