In Section 15 we defined a function to be superharmonic if its negative is subharmonic. This is equivalent to saying that F is superharmonic on the open set Ω in ℝn if for every xo ∈ Ω ∃ r(x0) > 0 with $$F\left( {x_0 } \right) \geqslant \frac{1} {A}\int\limits_{\left| {x - x_0 } \right| = a} {F\left( x \right)} dS,$$ (17.1) for all a < r(x0), where A is the area of the sphere {x| |x-x0| = a}, and $$\frac{{lim}} {{x \to x_0 }}F\left( x \right) \geqslant F\left( {x_0 } \right), for all x_0 \in \Omega .$$ (17.2) on any ball.