Abstract

A corollary of Gleason's theorem asserts that if the lattice of propositions of a physical system is isomorphic to the lattice of subspaces of a Hilbert space of dimension greater than two, then there is no probability measure that assigns only the values 1 and 0 (truth and falsity, respectively) to each of the propositions. Belinfante outlined an elegant geometrical proof of this corollary but relied upon an unrigorous measure-theoretical statement. An amplified geometrical proof is given along Belinfante's lines, but dispensing with measure theory