Intrinsically Lipschitz functions with normal target in Carnot groups

We provide a Rademacher theorem for intrinsically Lipschitz functions $phi:Usubseteq mathbb Wto mathbb L$, where $U$ is a Borel set, $mathbb W$ and $mathbb L$ are complementary subgroups of a Carnot group, where we require that $mathbb L$ 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.