  We study the density of states of two-dimensional electron gas in magnetic
field with scattering on point-like impurities that are uniformly distributed
along the sample. We show that the electron-impurity interaction completely
lifts the degeneracy of the Landau levels even at low impurity concentration.
This statement is in contradiction with the previous results obtained in the
unphysical approximation of two-dimensional impurities. There is a large region
of the electron energy $\omega $, counted from the Landau level, where the
density of states $\rho (\omega)$ is inversely proportional to $|\omega|$ and
proportional to the impurity concentration. Our results are applicable to
different 2D electron systems as heterostructures, inversion layers and
interfaces.
