Let $u$ be a continuous function on an open set $U$ of the complex plane. We say that $u$ satisfies the circle mean value property at a point $z_0\in U$ if $ u(z_0)=\frac{1}{2\pi}\int_0^{2\pi}u(z_0+re^{i\theta})d\theta$
for all $r$ sufficiently small such that the disc centered at $z_0$ with radius $r$> is contained in $U$. We say that $u$ satisfies the disc mean value property at a point $z_0$ if $u(z_0)=\frac{1}{\pi r^2}\iint_{D(z_0,r)}u dxdy$
I think the two properties are related. In particular i'd like to show that the first implies the second. Is this an application of Green's Thm maybe?