Muon bremsstrahlung photons converted in front of the DELPHI main tracker (TPC) in dimuon events at LEP1 were studied in two photon kinematic ranges: 0.2 < E_gamma <= 1 GeV and transverse momentum with respect to the parent muon p_T < 40 MeV/c, and 1 < E_gamma <= 10 GeV and p_T < 80 MeV/c . A good agreement of the observed photon rate with predictions from QED for the muon inner bremsstrahlung was found, contrary to the anomalous soft photon excess that has been observed recently in hadronic Z^0 decays. The obtained ratios of the observed signal to the predicted level of the muon bremsstrahlung are 1.06 +/- 0.12 +/- 0.07 in the photon energy range 0.2 < E_gamma <= 1 GeV and 1.04 +/- 0.09 +/- 0.12 in the photon energy range 1 < E_gamma <= 10 GeV. The bremsstrahlung dead cone is observed for the first time in the direct photon production at LEP.
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