Abstract
Some general properties of the density of states in the coherent potential approximation are derived. The basic result is a general explicit formula for the integrated density of states. Particular attention is paid to the variational properties of this formula and to its direct consequences. It is then applied to prove quite generally the sum rule for the number of states contained in the sub-bands of an n-component alloy. Finally, a discussion of the position of the band-edges is given. These band-edges are proved to be actually within the allowed bounds for disordered systems.