  We show that recent improvements in the $O(\alpha)$ long-distance quantum
electrodynamics (QED) corrections to the radiative inclusive $K_{e3}$ decay
rate using the Sirlin representation are free from infrared divergences and
collinear electron mass singularities in the limit $m_e\rightarrow0$, as
predicted by the Kinoshita-Lee-Nauenberg theorem. We also verify that in
massless QED with the simultaneous dimensional regularization of QED photon
infrared divergences and electron mass singularities leads to the same result
for the inclusive rate in the limit of four space-time dimensions. The
equivalence of the two approaches results in part from an interesting interplay
between a small chirality-breaking effect in the massless electron limit and
the generalization of space-time algebra and phase space integrals to $d>4$
dimensions. Our finding supports the small theoretical uncertainty claimed for
$K_{e3}$ radiative inclusive rates and reaffirms its utility in precision
unitarity tests of the quark mixing matrix.
