# pluripolar set

###### Definition.

Let $G\subset {\u2102}^{n}$ and let
$f:G\to \mathbb{R}\cup \{-\mathrm{\infty}\}$ be a plurisubharmonic
function^{} which is not identically $-\mathrm{\infty}$.
The set $\mathcal{P}:=\{z\in G\mid f(z)=-\mathrm{\infty}\}$ is
called a pluripolar set.

If $f$ is a holomorphic function^{} then $\mathrm{log}|f|$ is a plurisubharmonic function. The zero set of $f$ is then
a pluripolar set.

## References

- 1 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.

Title | pluripolar set |
---|---|

Canonical name | PluripolarSet |

Date of creation | 2013-03-22 14:29:15 |

Last modified on | 2013-03-22 14:29:15 |

Owner | jirka (4157) |

Last modified by | jirka (4157) |

Numerical id | 5 |

Author | jirka (4157) |

Entry type | Definition |

Classification | msc 32U05 |

Classification | msc 31C10 |