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单词 PolarSet
释义

polar set


Definition.

Let Gn and letf:G{-} be a subharmonicfunction which is not identically -.The set 𝒫:={xGf(x)=-} iscalled a polar set.

Proposition.

Let G and P be as above and suppose that g is acontinuousMathworldPlanetmathPlanetmathsubharmonic function on GP. Then g is subharmonicon the entire set G.

The requirement that g is continuous cannot be relaxed.

Proposition.

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

References

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