Calculus of Variations and Geometric Measure Theory
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M. Capolli - A. Pinamonti - G. Speight

A $C^k$ Lusin approximation theorem for real-valued functions on Carnot Groups

created by pinamonti on 27 Jul 2021
modified on 10 Jun 2022


Accepted Paper

Inserted: 27 jul 2021
Last Updated: 10 jun 2022

Journal: Indiana Univ. Math. J.
Year: 2021


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.


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