Inserted: 27 jul 2021
Last Updated: 10 jun 2022
Journal: Indiana Univ. Math. J.
We study the Lusin approximation problem for real-valued mea- surable functions on Carnot groups. We prove that k-approximate differen- tiability almost everywhere is equivalent to admitting a Lusin approximation by $C^k$ maps. We also prove that existence of an approximate (k − 1)-Taylor G polynomial almost everywhere is equivalent to admitting Lusin approximation by maps in a suitable Lipschitz function space.