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?

1$\begingroup$ Except a constant multiple which depends on the dimension. $\endgroup$– Alexandre EremenkoOct 31, 2018 at 13:33
1 Answer
See W.K. Hayman and P.B. Kennedy, Subharmonic functions, Vol. I, London...San Francisco, Academic Press. 1976, 3.5.4 ( Ch.3, Par. 5, Point 4) to this end.