*Accepted Paper*

**Inserted:** 5 jun 2020

**Last Updated:** 31 mar 2021

**Journal:** Ann. Acad. Sci. Fenn. Math.

**Year:** 2020

**Abstract:**

We provide a Rademacher theorem for intrinsically Lipschitz functions $\phi:U\subseteq \mathbb W\to \mathbb L$, where $U$ is a Borel set, $\mathbb W$ and $\mathbb L$ are complementary subgroups of a Carnot group, where we require that $\mathbb W$ is a Carnot subgroup and $\mathbb L$ is a normal subgroup. Our hypotheses are satisfied for example when $\mathbb W$ is a horizontal subgroup. Moreover, we provide an area formula for this class of intrinsically Lipschitz functions.

**Tags:**
GeoMeG