 Note that the simple random variables on \(\mathcal{A}\) correspond exactly to the simple random variables on \(\mathcal{A}^{\sim}\), and that these, in turn, correspond to some of the simple random variables (in the usual sense) on the measurable space \(S(\mathcal{A}^{\sim}\)). Thus, we have the following picture: The model \((\mathcal{A},\Delta)\) can always be obtained from a classical model simply by omitting some random variables, and identifying outcomes that can no longer be distinguished by those that remain.