| 词条 | Rademacher's theorem |
| 释义 |
In mathematical analysis, Rademacher's theorem, named after Hans Rademacher, states the following: If {{mvar|U}} is an open subset of {{math|Rn}} and {{math|f : U → Rm}} is Lipschitz continuous, then {{mvar|f}} is differentiable almost everywhere in {{mvar|U}}; that is, the points in {{mvar|U}} at which {{mvar|f}} is not differentiable form a set of Lebesgue measure zero. GeneralizationsThere 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
References
| last = Federer | first = Herbert | authorlink = Herbert Federer | title = Geometric measure theory | place= Berlin–Heidelberg–New York | publisher = Springer-Verlag | series = Die Grundlehren der mathematischen Wissenschaften | volume = 153 | year = 1969 | pages = xiv+676 | isbn = 978-3-540-60656-7 | id= | mr=0257325 | zbl= 0176.00801 }}. (Rademacher's theorem is Theorem 3.1.6.)
2 : Lipschitz maps|Theorems in measure theory |
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