[@gaboriau], i.e. a measurable assignment $X\ni x\mapsto\Sigma_x$ of simplicial complexes together with an $\mathcal{R}$-action: For every $(x,y)\in\mathcal{R}$ there is a simplicial isomorphism $\psi_{x,y}\colon\Sigma_x\to \Sigma_y$ such that $\psi_{x,y}\circ \psi_{y,z}=\psi_{x,z}$ and $\psi_{x,x}={\operatorname{Id}}_{\Sigma_x}$. Further assume there is a Borel fundamental domain $F$ for the action on the vertices with a countable partition $F=\bigsqcup_{j\in J}F_j$ such that the projection $\pi\colon F\to X$ is injective on each $F_j$ and $\sum_J \nu(\pi(F_j))<\infty$. Then this defines a unimodular [*rrsc*]{}: $$\begin{aligned}
    \mu_{\Sigma,\mathcal{R}}(A)\coloneqq\frac{\sum_{j\in J}\nu\left(\pi(\{f\in F_j\;|\;[\Sigma_{\pi(f)},f]\in A\})\right)}{\sum_{j\in J}\nu(\pi (F_j))},\end{aligned}$$ for all Borel sets $A$. A special case of this is a field of graphs $x\mapsto \Phi_x$ defined by a graphing $\Phi$ of $\mathcal{R}$. In this case the fundamental domain is just the diagonal $(x,x)\in \mathcal{R}$ and the random rooted graph is given by $$\begin{aligned}
    \mu_{\Phi,\mathcal{R}}(A)=\nu\left(\{x\in X\;|\; [\Phi(x),x]\in A\}\right).\end{aligned}$$ Random rooted graphs defined by graphings were also treated in [@aldous-lyons]. For more information about measured equivalence relations see [@feldman-mooreI; @feldman-mooreII].

4.  The different models of random simplicial complexes, like the Erdös-Rényi model $G(n,p)$, the random $d$-complex $Y_d(n,p)$ of Linial and Meshulam [@linial-meshulam], random flag complexes $X(n,p)$ [@kahle] or random geometric complexes (e.g. the random geometric graph of Penrose [@penrose]) give rise to unimodular measures on ${\mathcal{SC}_*}$ by applying the construction of 