Théorème de Rademacher

Rademacher's theorem In mathematical analysis, Théorème de Rademacher, named after Hans Rademacher, states the following: If U is an open subset of Rn and f: U → Rm is Lipschitz continuous, then f is differentiable almost everywhere in U; C'est, the points in U at which f is not differentiable form a set of Lebesgue measure zero.

Generalizations There is a version of Rademacher's theorem that holds for Lipschitz functions from a Euclidean space into an arbitrary metric space in terms of metric differentials instead of the usual derivative.

See also Alexandrov theorem Pansu derivative References Federer, Herbert (1969), Geometric measure theory, Les enseignements fondamentaux des sciences mathématiques, volume. 153, Berlin–Heidelberg–New York: Springer Verlag, pp. xiv+676, ISBN 978-3-540-60656-7, M 0257325, Zbl 0176.00801. (Rademacher's theorem is Theorem 3.1.6.) Heinonen, Juha (2004). "Lectures on Lipschitz Analysis" (PDF). Lectures at the 14th Jyväskylä Summer School in August 2004. (Rademacher's theorem with a proof is on page 18 and further.) Cet article lié à l'analyse mathématique est un bout. Vous pouvez aider Wikipédia en l'agrandissant.

Catégories: Lipschitz mapsTheorems in measure theoryMathematical analysis stubs