Abstract
Let
u
be a plurisubharmonic function, defined on a neighbourhood of a point
x,
such that the complex Monge-Ampère operator is well-defined on
u.
Suppose also that
u
has a weak singularity, in the sense that the Lelong number of
u
at
x
vanish. Is it true that the residual mass of the measure
(d
d
c
u
)
n
vanish at
x
?
To our knowledge there is no known example that falsifies the posed question. In this paper some partial results are obtained. We find that for a significant subset of plurisubharmonic functions with well defined Monge-Ampère mass vanishing Lelong number does implies vanishing residual mass of the Monge-Ampère measure.