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
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 differential
s instead of the usual derivative.
* . ''(Rademacher's theorem is Theorem 3.1.6.)''
* ''(Rademacher's theorem with a proof is on page 18 and further.)''
Category:Theorems in measure theory