 As noted above, Gleason's theorem shows that there is no probability measure over the rays of a Hilbert space that only takes the values 0 and 1 (as long as the dimension of that space exceeds 2).The Kochen–Specker theorem refines this statement by constructing a specific finite subset of rays on which no such probability measure can be defined.The fact that such a finite subset of rays must exist follows from Gleason's theorem by way of a logical compactness argument, but this method does not construct the desired set explicitly.