Gleason's theorem (named after Andrew M. Gleason) is a mathematical result which is of particular importance for the field of quantum logic. It proves that the Born rule for the probability of obtaining specific results for a given measurement follows naturally from the structure formed by the lattice of events in a real or complex Hilbert space. The theorem states:

Theorem. Suppose H is a separable Hilbert space of complex dimension at least 3. Then for any quantum probability measure on the lattice Q of self-adjoint projection operators on H there exists a unique trace class operator W such that P(E) = Tr(W E) for any self-adjoint projection E in Q.