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We calculate the branching ratios of the $K^+ \to \pi^0 l^+ \nu_l\gamma (l =e, \mu)$ decays, and the T-odd triple momenta correlations$\xi=\vec{q}\cdot[\vec{p}_l \times \vec{p}_\pi]/M^3_K$, due to theelectromagnetic final state interaction, in these processes. The contributionson the order of $\omega^{-1}$ and $\omega^0$ to the corresponding amplitudesare treated exactly. For the branching ratios, the corrections on the order of$\omega$ are estimated and demonstrated to be small. We compare the resultswith those of other authors. In some cases our results differ considerably fromthe previous ones.

$K^+_{l3\gamma}$ decays revisited: branching ratios and T-odd momenta correlations