Let U⊆C be an open set and f a real-valued continuous function on U. Suppose that for each closed disk D^_(P, r)⊆U and every real-valued harmonic function h defined on a neighborhood of D^_(P, r) which satisfies f<=h on dD(P, r), it holds that f<=h on the open disk D(P, r). Then f is said to be subharmonic on U. 1. If f_1, f_2 are subharmonic on U, then so is f_1 + f_2. 2. If f_1 is subharmonic on U and a>0 is a constant, than a f_1 is subharmonic on U.

barrier | harmonic function