  We study the Lusin approximation problem for real-valued measurable functions
on Carnot groups. We prove that k-approximate differentiability almost
everywhere is equivalent to admitting a Lusin approximation by
$C^{k}_{\mathbb{G}}$ maps. We also prove that existence of an approximate
(k-1)-Taylor polynomial almost everywhere is equivalent to admitting a Lusin
approximation by maps in a suitable Lipschitz function space.
