The K^+ to pi^0 mu^+ u gamma ($K_{mu 3 gamma}$) decay has been measured with stopped positive kaons at the KEK 12 GeV proton synchrotron. A $K_{mu 3 gamma}$ sample containing 125 events was obtained. The partial branching ratio $Br(K_{mu 3 gamma}, E_{gamma}>30 {rm MeV}, theta_{mu^+ gamma}>20^{circ})$ was found to be $[2.4 pm 0.5(stat) pm 0.6(syst)]times 10^{-5}$, which is in good agreement with theoretical predictions.
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