  In Thurston's notes, he gives two different definitions of the Gromov norm
(also called simplicial volume) of a manifold and states that they are equal
but does not prove it. Gromov proves it in the special case of hyperbolic
manifolds as a consequence of his proof that simplicial volume is proportional
to volume. We give a proof for all differentiable manifolds.
  This version corrects a few typos in an earlier version and formally proves
the theorem for differentiable manifolds rather than locally finite simplicial
complexes (but very few actual changes have been made).
