2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59810It was pointed out to us that the proof of a crucial lemma (Lemma 5.3) in the paper is incorrect. Thus the approximation theorem (Theorem 0.1) for L^2 torsion of an amenable covering of a finite simplicial complex remains unproved. However, results and proofs of the first four sections (in particular, the approximation theorem (Theorem 0.3) for the spectral density function of an amenable covering) are correct.withdrawn by the authorsDifferential Geometry58G11; 58G18; 58G25text