Pluripolar set
In mathematics, in the area of potential theory, a pluripolar set is the analog of a polar set for plurisubharmonic functions.Definition
Let and let be a plurisubharmonic function which is not identically. The set
is called a complete pluripolar set. A pluripolar set is any subset of a complete pluripolar set. Pluripolar sets are of Hausdorff dimension at most and have zero Lebesgue measure.
If is a holomorphic function then is a plurisubharmonic function. The zero set of is then a pluripolar set.
