 If \(\mathcal{A}\) is a test space with outcome-space \(X\), a state on \(\mathcal{A}\) is a mapping \(\omega : X \rightarrow\) [0,1] such that \(\sum_{x\in E} \omega(x) = 1\) for every test \(E \in \mathcal{A}\). Thus, a state is a consistent assignment of a probability weight to each test—consistent in that, where two distinct tests share a common outcome, the state assigns that outcome the same probability whether it is secured as a result of one test or the other. (This may be regarded as a normative requirement on the outcome-identifications implicit in the structure of \(\mathcal{A}\): if outcomes of two tests are not equiprobable in all states, they ought not to be identified.) The set of all states on \(\mathcal{A}\) is denoted by \(\Omega(\mathcal{A})\). This is a convex set, but in contrast to the situation in discrete classical probability theory, it is generally not a simplex.