*Published Paper*

**Inserted:** 8 feb 2016

**Last Updated:** 16 may 2017

**Journal:** Calculus of Variations and Partial Differential Equations

**Volume:** 55

**Number:** 5

**Pages:** 1-22

**Year:** 2016

**Abstract:**

A Carnot group $\mathbb{G}$ admits Lusin approximation for horizontal curves if for any absolutely continuous horizontal curve $\gamma$ in $\mathbb{G}$ and $\varepsilon>0$, there is a $C^1$ horizontal curve $\Gamma$ such that $\Gamma=\gamma$ and $\Gamma'=\gamma'$ outside a set of measure at most $\varepsilon$. We verify this property for free Carnot groups of step 2 and show that it is preserved by images of Lie group homomorphisms preserving the horizontal layer. Consequently, all step 2 Carnot groups admit Lusin approximation for horizontal curves.

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