polar set


Let Gn and let f:G{-} be a subharmonic function which is not identically -. The set 𝒫:={xGf(x)=-} is called a polar set.


Let G and P be as above and suppose that g is a continuousMathworldPlanetmathPlanetmath subharmonic function on GP. Then g is subharmonic on the entire set G.

The requirement that g is continuous cannot be relaxed.


Let G and P be as above. Then the Lebesgue measureMathworldPlanetmath of P is 0.


  • 1 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
Title polar set
Canonical name PolarSet
Date of creation 2013-03-22 14:29:13
Last modified on 2013-03-22 14:29:13
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 6
Author jirka (4157)
Entry type Definition
Classification msc 31C05
Classification msc 31B05
Classification msc 31A05