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Date: 11-6-2018
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Let be an open set and a real-valued continuous function on . Suppose that for each closed disk and every real-valued harmonic function defined on a neighborhood of which satisfies on , it holds that on the open disk . Then is said to be subharmonic on (Krantz 1999, p. 99).
1. If are subharmonic on , then so is .
2. If is subharmonic on and is a constant, than is subharmonic on .
3. If are subharmonic on , then is also subharmonic on .
REFERENCES:
Krantz, S. G. "The Dirichlet Problem and Subharmonic Functions." §7.7 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 97-101, 1999.
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