 Gleason's theorem can be extended to some cases where the observables of the theory form a von Neumann algebra.Specifically, an analogue of Gleason's result can be shown to hold if the algebra of observables has no direct summand that is representable as the algebra of 2×2 matrices over a commutative von Neumann algebra (i.e., no direct summand of type "I"2).In essence, the only barrier to proving the theorem is the fact that Gleason's original result does not hold when the Hilbert space is that of a qubit.