Category:Definitions/Superharmonic Functions

This category contains definitions related to Superharmonic Functions.
Related results can be found in Category:Superharmonic Functions.

Let $D$ be a complex domain.

A superharmonic function is a continuous real-valued function $f$ such that for every closed disk $\map {B^-} {a; r} \subseteq D$ with center $a$ and radius $r$:

$\ds \map f a \ge \int_0^{2 \pi} \map f {a + r e^{i \theta} } \rd \theta$