The structure dependent radiative $K^+ rightarrow e^+ u gamma$ ($K_{e2gamma}^{rm SD}$) decay was investigated with stopped positive kaons. The $e^+$ momentum spectra were measured with and without a photon in coincidence and analyzed with Monte Carlo simulations for acceptance and detector response to extract the ratio of the $K_{e2gamma}^{rm SD}$ and $K^+ rightarrow e^+ u$ ($K_{e2}$) branching ratios. A value of $Br(K_{e2gamma}^{rm SD}) / Br(K_{e2}) = 1.22pm0.07_{rm stat} pm 0.04_{rm syst}$ was obtained, which is significantly larger than the value inferred from a previous experimental result for $Br(K_{e2gamma}^{rm SD})/Br(K^+rightarrow mu^+ u)$.
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