Definition of Haar systems, especially for groupoids $C^*$-algebra

Question

In A Groupoid approach to $C^*$-algebras Jean Renault introduces left Haar systems. Say $G$ is a groupoid. Let $\Lambda=\{\mu^u,\,\,:\,\,u\in G^0\}$ be a family of Haar measures on $G$. Renault requires that the support of $\mu^u$ equals $G^u$, or in other words say $t$ is the target map then $t^{-1}(u)=\text{supp}(\mu^u)$. Yet I don't really see how this works as $t^{-1}(u)$ only consists of one set, has any one seen this definition before and can help me get some intuition for this?