  The Landau, Pomeranchuk, Migdal (LPM) effect (suppression of the
bremsstrahlung from high energy electron due to a multiple scattering of an
emitting electron in dense media) is considered for the case when thickness of
a target is of the order or less than the formation length of radiation. The
effects of the polarization of a medium and transition radiation are taken into
account as well. Qualitative picture of the phenomenon is discussed in detail.
Comparison with recent experimental data is carried out.
