The bremsstrahlung of photons from highly relativistic electrons is investigated. The cross section of the process, which is suppressed due to the multiple scattering of an emitting electron in dense media ͑the LPM effect͒ and due to photon interaction with electrons of a medium, is calculated with an accuracy up to the ''next to leading logarithm'' and with the Coulomb corrections taken into account. Making allowances for multiple scattering and the polarization of the medium, an analysis of the radiation on a target boundary is carried out. The method of the consideration of radiation in a thin target under the influence of the LPM effect is developed. The interrelation with recent experiments is discussed. ͓S0556-2821͑98͒04203-9͔
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