  We discuss the problem of a possible "violation" of the optical sum rule in
the normal (non superconducting) state of strongly correlated electronic
systems, using our recently proposed DMFT+Sigma approach, applied to two
typical models: the "hot - spot" model of the pseudogap state and disordered
Anderson - Hubbard model. We explicitly demonstrate that the general Kubo
single band sum rule is satisfied for both models. However, the optical
integral itself is in general dependent on temperature and characteristic
parameters, such as pseudogap width, correlation strength and disorder
scattering, leading to effective "violation" of the optical sum rule, which may
be observed in the experiments.
