polar set
Definition.
Let and let be a subharmonicfunction which is not identically .The set iscalled a polar set.
Proposition.
Let and be as above and suppose that is acontinuoussubharmonic function on . Then is subharmonicon the entire set .
The requirement that is continuous cannot be relaxed.
Proposition.
Let and be as above. Then the Lebesgue measure of is 0.
References
- 1 Steven G. Krantz.,AMS Chelsea Publishing, Providence, Rhode Island, 1992.