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In mathematical analysis, Rademacher's theorem, named after Hans Rademacher, states the following: If is an open subset of and is Lipschitz continuous, then is differentiable almost everywhere in ; that is, the points in at which 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


* . ''(Rademacher's theorem is Theorem 3.1.6.)'' * ''(Rademacher's theorem with a proof is on page 18 and further.)'' Category:Lipschitz maps Category:Theorems in measure theory {{mathanalysis-stub