2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147621In this paper, we prove that the $L^2$ Betti numbers of an amenable covering space can be approximated by the average Betti numbers of a regular exhaustion, proving a conjecture that we made in an earlier paper. We also prove that an arbitrary amenable covering space of a finite simplicial complex is of determinant class.14 pages, AMS-LaTeX, a minor revision of an earlier version containing new references to earlier work in the fieldDifferential Geometrytext