  We use the mean value property in an asymptotic way to provide a notion of a
pointwise Laplacian, called AMV Laplacian, that we study in several contexts
including the Heisenberg group and weighted Lebesgue measures. We focus
especially on a class of metric measure spaces including intersecting
submanifolds of $\mathbb{R}^n$, a context in which our notion brings new
insights; the Kirchhoff law appears as a special case. In the general case, we
also prove a maximum and comparison principle, as well as a Green-type identity
for a related operator.
