 An important consequence of Gleason’s Theorem is that \(L(\mathbf{H})\) does not admit any probability measures having only the values 0 and 1. To see this, note that for any density operator \(W\), the mapping \(u \rightarrow \langle Wu,u\rangle\) is continuous on the unit sphere of \(\mathbf{H}\). But since the latter is connected, no continuous function on it can take only the two values 0 and 1. This result is often taken to rule out the possibility of “hidden variables”—an issue taken up in more detail in section 6.