  We show that Nachman's integral equations for the Calder\'on problem, derived
for conductivities in $W^{2,p}(\Omega)$, still hold for $L^\infty$
conductivities which are $1$ in a neighborhood of the boundary. We also prove
convergence of scattering transforms for smooth approximations to the
scattering transform of $L^\infty$ conductivities. We rely on
Astala-P\"aiv\"arinta's formulation of the Calder\'on problem for a framework
in which these convergence results make sense.
