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
.