A Lelong number measures the logarithmic singularity of a plurisubharmonic function, or the
local concentration of an associated positive current. For a plurisubharmonic potential
near 
, the function convention is
 |
Thus 
has Lelong number 
for 
, while a locally bounded potential
has Lelong number zero. Smooth changes of potential do not affect the number.
For the local weights of a semipositive singular Hermitian metric, zero Lelong numbers everywhere rule out logarithmic poles.
They imply local integrability of 
for every fixed 
.
