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The main result is a general approximation theorem for normalised Betti numbers for Farber sequences of lattices in totally disconnected groups. Further, we contribute to the general theory of    L  2   ‐Betti numbers of totally disconnected groups and provide exact computations of the    L  2   ‐Betti numbers of the Neretin group and Chevalley groups over the field of Laurent series over a finite field and their lattices.

L 2 ‐Betti numbers of totally disconnected groups and their approximation by Betti numbers of lattices