In mathematics, in the area of potential theory, a pluripolar set is the analog of a polar set for plurisubharmonic functions.
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. [1]
If is a holomorphic function then is a plurisubharmonic function. The zero set of is then a pluripolar set.
This article incorporates material from pluripolar set on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.
In mathematics, in the area of potential theory, a pluripolar set is the analog of a polar set for plurisubharmonic functions.
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. [1]
If is a holomorphic function then is a plurisubharmonic function. The zero set of is then a pluripolar set.
This article incorporates material from pluripolar set on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.