In mathematical analysis, a metric differential is a generalization of a derivative for a Lipschitz continuous function defined on a Euclidean space and taking values in an arbitrary metric space.
With this definition of a derivative, one can generalize Rademacher's theorem to metric space-valued Lipschitz functions.
If f is a function from a Euclidean space Rn that takes values instead in a metric space X, it doesn't immediately make sense to talk about differentiability since X has no linear structure a priori.
Even if you assume that X is a Banach space and ask whether a Fréchet derivative exists almost everywhere, this does not hold.
A theorem due to Bernd Kirchheim[1] states that a Rademacher theorem in terms of metric differentials holds: for almost every z in Rn, MD(f, z) is a seminorm and The little-o notation employed here means that, at values very close to z, the function f is approximately an isometry from Rn with respect to the seminorm MD(f, z) into the metric space X.