Satz von Rademacher

Rademacher's theorem In mathematical analysis, Satz von 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; das ist, 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, Die Grundlehren der mathematischen Wissenschaften, vol. 153, Berlin–Heidelberg–New York: Springer-Verlag, pp. xiv+676, ISBN 978-3-540-60656-7, HERR 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.) Dieser Artikel zur mathematischen Analyse ist ein Stummel. Sie können Wikipedia helfen, indem Sie es erweitern.

Kategorien: Lipschitz mapsTheorems in measure theoryMathematical analysis stubs