get that the limit of normalized Betti numbers of a Benjamini-Schramm convergent sequence $K_n$ of finite simplicial complexes of uniformly bounded degree exists, which is a result of Elek [@elek], and the limit is the $\ell^2$-Betti number of the limit measure.\
This result generalizes Lück’s approximation Theorem [@lueck], which says in its classical version that for a free $\Gamma$-CW-complex $X$, with $\Gamma\backslash X$ of finite type, $$\lim_{i\to\infty}\frac{b_p(\Gamma_i\backslash X;\mathbb{Q})}{[\Gamma:\Gamma_i]}=\beta_p^{(2)}(X,\Gamma)$$ holds for all finite index normal towers $(\Gamma_i)_{i\in{{\mathbb N}}}$. Farber [@farber] extended this to so called Farber sequences, which weakens the assumption that $(\Gamma_i)_{i\in{{\mathbb N}}}$ is normal. Elek and Szabó [@elek-szabo] further extended this result to normal towers $(\Gamma_i)_{i\in{{\mathbb N}}}$ such that $\Gamma/\Gamma_i$ is sofic for every $i\in {{\mathbb N}}$. In [@7s] Abert, Bergeron, Biringer, Gelander, Nikolov, Raimbault and Samet proved an approximation result for Benjamini-Schramm convergent sequences of orbifolds which arise from a uniformly discrete sequence of lattices in a semi-simple Lie group. Petersen, Sauer and Thom generalized the notion of Farber sequences to lattices in a totally disconnected, second countable unimodular group $G$, which is also a instance of local weak convergence and proved that the normalized Betti numbers of a uniformly discrete Farber sequence converge to the $\ell^2$-Betti number 