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Rademacher's theorem : ウィキペディア英語版
Rademacher's theorem
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.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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