A note on the inverse maximum principle on Carnot groups

Let $\Delta_{\G}$ be a sublaplacian on a Carnot group, and let $\mu$ be a local measure on the open set $\Omega \subset \G$. If $u\in L^1_{loc}(\Omega)$ is such that\r\n$$-\Delta_{\G} u= \mu, \; u\ge 0 \quad \hbox{on} \ \Omega,$$\r\nthen $\mu_c\ge 0$, where $\mu_c$ is the concentrate component of $\mu$ with\r\nrespect to the $\G$-capacity.\r\nThis extends to the Carnot group setting a result contained in \cite{DuPo04}.