The mean value theorem for harmonic functions in a domain of Hilbert space

We prove that the value of any harmonic function whose domain is an open set in the Hilbert space in a given point $x$ is equal to the mean value of the function with respect to a measure given on a ball with the centre $x$. From this we derive a theorem of Liouville that says that a bounded harmonic function defined in all points of a Hilbert space is constant.