  We extend the isospectral deformations of Connes, Landi and Dubois-Violette
to the case of Riemannian spin manifolds carrying a proper action of the
noncompact abelian group $R^l$. Under deformation by a torus action, a standard
formula relates Dixmier traces of measurable operators to integrals of
functions on the manifold. We show that this relation persists for actions of
$R^l$, under mild restrictions on the geometry of the manifold which guarantee
the Dixmier traceability of those operators.
