Let $B(x\_{0},r)$ be the ball of center $ x\_{0} $ and radius $r>0$ in $ \mathbb{R}^{k} $ ($ k\geq2 $), and $u$ a subharmonic function on an open neighborhood of the closure of $B(x\_{0},r)$. Let $\mu$ be the Riesz measure of $u$ on this ball. If $u$ is $C^{2}-$smooth, is it true that $\mu=\Delta u$, the laplacian of $u$? Do you know a reference for that?



Riesz measure of a smooth subharmonic function on a ball
See [W.K. Hayman and P.B. Kennedy, Subharmonic functions, Vol. I, London-...-San Francisco, Academic Press. 1976](https://zbmath.org/?q=an%3A0419.31001), 3.5.4 ( Ch.3, Par. 5, Point 4) to this end.


