Pluripolar set - Alchetron, The Free Social Encyclopedia

In mathematics, in the area of potential theory, a pluripolar set is the analog of a polar set for plurisubharmonic functions.

Definition

Let G ⊂ C n and let f : G → R ∪ { − ∞ } be a plurisubharmonic function which is not identically − ∞ . The set

P := { z ∈ G ∣ f ( z ) = − ∞ }

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 2 n − 2 and have zero Lebesgue measure.

If f is a holomorphic function then log ⁡ | f | is a plurisubharmonic function. The zero set of f is then a pluripolar set.

References

Pluripolar set Wikipedia

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