  A model-independent expression for the Dalitz plot of the semileptonic decays
of a neutral kaon $K_{\mu 3}^0$, including radiative corrections to order
$\mathcal{O}[(\alpha / \pi )(q/M_1)]$, where $q$ is the four-momentum transfer
and $M_1$ is the mass of the decaying kaon, is presented. In this paper the
emitted muon is considered to be polarized so the analysis is centered on
numerically evaluating the radiative corrections to the longitudinal,
transverse, and normal polarization muon components. The model dependence of
radiative corrections is kept in general form within this approximation, which
is useful for model-independent experimental analyses. The final expressions,
with the triple integration of the bremsstrahlung photon variables are ready to
be performed numerically. The radiative corrections to the components of the
muon polarization are found to be very small compared to their respective
uncorrected values.
