  The structure dependent radiative $K^+ \rightarrow e^+ \nu \gamma$
($K_{e2\gamma}^{\rm SD^+}$) decay was investigated with stopped positive kaons.
The $e^+$ momentum spectra containing 574$\pm$30 $K_{e2\gamma}^{\rm SD^+}$
events with a $K^+ \rightarrow \mu^+ \nu$ ($K_{\mu2}$) background of 28$\pm$19
events 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 branching ratio of the $K_{e2\gamma}^{\rm SD^+}$ decay and the
$K^+ \rightarrow e^+ \nu$ decay including the internal bremsstrahlung process
($K_{e2(\gamma)}$). A value of $Br(K_{e2\gamma}^{\rm SD^+}) /
Br(K_{e2(\gamma)}) = 1.12\pm0.07_{\rm stat} \pm 0.04_{\rm syst}$ was obtained.
This indicates a partial branching ratio, $Br(K_{e2\gamma}^{\rm SD^+},
~{p_e>200~{\rm MeV}/c}, ~{E_\gamma>10~{\rm MeV}})/Br(K_{\mu2}) =(1.85 \pm
0.11_{\rm{stat}} \pm 0.07_{\rm{syst}}) \times10^{-5}$, which is
$25\%(\sim$2.5$\sigma)$ higher than the previous experimental result.
