Radon–Nikodym Property and Area Formula for Banach Homogeneous Group Targets

We prove a Rademacher-type theorem for Lipschitz mappings from a subset of a Carnot group to a Banach homogeneous group, equipped with a suitably weakened Radon–Nikodym property. We provide a metric area formula that applies to these mappings and more generally to all almost everywhere metrically differentiable Lipschitz mappings defined on a Carnot group.