  We study mean value properties of harmonic functions in metric measure
spaces. The metric measure spaces we consider have a doubling measure and
support a (1,1)- Poincar\'e inequality. The notion of harmonicity is based on
the Dirichlet form defined in terms of a Cheeger differentiable structure. By
studying fine properties of the Green function on balls, we characterize
harmonic functions in terms of a mean value property. As a consequence, we
obtain a detailed description of Poisson kernels. We shall also obtain a
Gauss-Green type formula for sets of finite perimeter which posses a Minkowski
content characterization of the perimeter. For the Gauss-Green formula we
introduce a suitable notion of the interior normal trace of a regular ball.
