Demailly–Lelong numbers on complex spaces

We prove a conjecture proposed by Berman–Boucksom–Eyssidieux–Guedj–Zeriahi, affirming that the Demailly–Lelong number can be determined through a combination of intersection numbers given by the divisorial part of the potential and the SNC divisors over a log resolution of the maximal ideal of a given point. Moreover, this result establishes a pointwise comparison of two different notions of Lelong numbers of plurisubharmonic functions defined on singular complex spaces. We also provide an estimate for quotient singularities and sharp estimates for two-dimensional ADE singularities.