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