  A self-consistent kinetic theory of Thomson scattering of an electromagnetic
field by a non-uniform plasma is derived. We draw the readers' attention to the
inconsistency in recent results on the Thomson scattering in inhomogeneous
plasma, which leads to violation of the Fluctuation-Dissipation Theorem. We
show that not only the imaginary part, but also the derivatives of the real
part of the dielectric susceptibility determine the amplitude and the width of
the Thomson scattering spectral lines. As a result of inhomogeneity, these
properties become asymmetric with respect to inversion of the sign of the
frequency. A method is proposed for measuring local gradients of the electron
density with the aid of Thomson scattering.
