QED one-loop corrections to radiative muon decay

Based upon the Fermi interaction, the differential decay rate of the radiative muon decay including one-loop radiative corrections is determined to the order ${G}_{F}^{2}{\ensuremath{\alpha}}^{2}$. Essential aspects of the calculation are exhibited. After cancellation of IR divergences, the double radiative muon decay is included. Some initial applications are considered.