On measures associated to superharmonic functions

Abstract:

Let u be a superharmonic function in an open set $\Omega$ in ${R^n}$ and let $\mu$ be the positive Radon measure associated to u, i.e. $\mu$ is a negative constant multiple of the distributional Laplacian $\Delta u$ of u. Using mostly elementary techniques, the paper deals with the properties of $\mu$ in the large, when $u > 0$ and $\Omega = {R^n}$, and in the small, in some neighbourhood of a point in $\Omega$.