  Let X be a smooth variety and J, K two ideal sheaves on X. We prove the
following formula relating the multiplier ideals of J, K and J+K: I(X,
c(J+K))\subset \sum_{a+b=c} I(X, aJ)\cdot I(X,bK). An analogous formula holds
for the asymptotic multiplier ideals of two graded systems of ideals. As a
consequence, we show how to approximate at any given point arbitrary multiplier
ideals by multiplier ideals of zero dimensional ideals. We apply this to study
the invariance of multiplier ideals under different embeddings.
