mean value property

Let a function h:U->R be continuous on an open set U⊆C. Then h is said to have the ϵ_(z_0)-property if, for each z_0 element U, there exists an ϵ_(z_0)>0 such that D^_(z_0, ϵ_(z_0))⊆U, where D^_ is a closed disk, and for every 0<ϵ<ϵ_(z_0), h(z_0) = 1/(2π) integral_0^(2π) h(z_0 + ϵ e^(i θ)) d θ. If h has the mean-value property, then h is harmonic.