 An operator expressible in this way as a convex combination of one-dimensional projections in is called a density operator. Density operators are the standard mathematical representation for general (pure or “mixed”) quantum-mechanical states. We have just seen that every density operator \(W\) gives rise to a countably additive probability measure on \(L(\mathbf{H})\). The following striking converse, due to A. Gleason [1957], shows that the theory of probability measures on \(L(\mathbf{H})\) is co-extensive with the theory of (mixed) quantum mechanical states on \(\mathbf{H}\):