  For a closed Riemannian manifold we extend the definition of analytic and
Reidemeister torsion associated to an orthogonal representation of fundamental
group on a Hilbert module of finite type over a finite von Neumann algebra. If
the representation is of determinant class we prove, generalizing the
Cheeger-M\"uller theorem, that the analytic and Reidemeister torsion are equal.
In particular, this proves the conjecture that for closed Riemannian manifolds
with positive Novikov-Shubin invariants, the L2 analytic and Reidemeister
torsions are equal.
