In mathematics, the Pansu derivative is a derivative on a Carnot group, introduced by Pierre Pansu (1989).
admits a one-parameter family of dilations,
are Carnot groups, then the Pansu derivative of a function
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.
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