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 .