  The basic ingredients of the consistent histories approach to quantum
mechanics are the space of histories and the space of decoherence functionals.
In this work we extend the classification theorem for decoherence functionals
proven by Isham, Linden and Schreckenberg to the case where the space of
histories is the lattice of projection operators on an arbitrary separable or
non-separable complex Hilbert space of dimension strictly greater than two.
