Riesz measure of a subharmonic function

Summary

The Riesz measure of a subharmonic function is its Laplacian taken in the sense of distributions, which is always a positive Radon measure. It records where and how strongly the function fails to be harmonic: it vanishes exactly on the open sets where the function is harmonic. Through the Riesz decomposition theorem, a subharmonic function is locally the potential of its Riesz measure plus a harmonic function. For $\log\abs{f}$ with $f$ holomorphic, the Riesz measure counts the zeros of $f$.