The number of states with energy E ′ (degree of degeneracy) is given by: g ( E ′ ) = lim Δ Δ E → → 0 ∫ ∫ E ′ E ′ + Δ Δ E D ( E ) d E = lim Δ Δ E → → 0 D ( E ′ ) Δ Δ E , where the last equality only applies when the mean value theorem for integrals is valid.