Pansu derivative

In mathematics, the Pansu derivative is a derivative on a Carnot group, introduced by . A Carnot group formula_1 admits a one-parameter family of dilations, formula_2. If formula_3 and formula_4 are Carnot groups, then the Pansu derivative of a function formula_5 at a point formula_6 is the function formula_7 defined by
provided that this limit exists.
A key theorem in this area is the Pansu–Rademacher theorem, a generalization of Rademacher's theorem, which can be stated as follows: Lipschitz continuous functions between (measurable subsets of) Carnot groups are Pansu differentiable almost everywhere.