  It 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.
