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In mathematics, the Pansu derivative is a derivative on a Carnot group, introduced by Pierre Pansu. A Carnot group admits a one-parameter family of dilations, . If and are Carnot groups, then the Pansu derivative of a function at a point is the 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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  • Derivada de Pansu (ca)
  • Pansu derivative (en)
  • Pansuderivata (sv)
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  • En matemàtiques, la derivada de Pansu és una derivada en un grup de Carnot i va ser introduïda per Pierre Pansu. Un grup de Carnot admet una família de dilacions d'un paràmetre, . Si i són grups de Carnot, llavors la derivada de Pansu d'una funció en un punt és la funció definida com sempre i quan aquest límit existeixi. Un teorema clau en aquesta àrea és el de Pansu-Rademacher, una generalització del teorema de Rademacher, que es pot afirmar com: "les funcions Lipschitz contínues entre (subconjunts mesurables de) grups de Carnot són derivables Pansu gairebé pertot." (ca)
  • In mathematics, the Pansu derivative is a derivative on a Carnot group, introduced by Pierre Pansu. A Carnot group admits a one-parameter family of dilations, . If and are Carnot groups, then the Pansu derivative of a function at a point is the 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. (en)
  • Inom matematiken är Pansuderivatan, introducerad av en derivata på en Carnotgrupp. (sv)
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  • En matemàtiques, la derivada de Pansu és una derivada en un grup de Carnot i va ser introduïda per Pierre Pansu. Un grup de Carnot admet una família de dilacions d'un paràmetre, . Si i són grups de Carnot, llavors la derivada de Pansu d'una funció en un punt és la funció definida com sempre i quan aquest límit existeixi. Un teorema clau en aquesta àrea és el de Pansu-Rademacher, una generalització del teorema de Rademacher, que es pot afirmar com: "les funcions Lipschitz contínues entre (subconjunts mesurables de) grups de Carnot són derivables Pansu gairebé pertot." (ca)
  • In mathematics, the Pansu derivative is a derivative on a Carnot group, introduced by Pierre Pansu. A Carnot group admits a one-parameter family of dilations, . If and are Carnot groups, then the Pansu derivative of a function at a point is the 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. (en)
  • Inom matematiken är Pansuderivatan, introducerad av en derivata på en Carnotgrupp. (sv)
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