  A pure state f of a von Neumann algebra M is called classically normal if f
is normal on any von Neumann subalgebra of M on which f is multiplicative.
Assuming the continuum hypothesis, a separably represented von Neumann algebra
M has classically normal, singular pure states iff there is a central
projection p in M such that Mp is a factor of type I_\infty, II, or III.
