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Alexandrov theorem : ウィキペディア英語版
Alexandrov theorem
In mathematical analysis, the Alexandrov theorem, named after Aleksandr Danilovich Aleksandrov, states that if is an open subset of and    is a convex function, then has a second derivative almost everywhere.
In this context, having a second derivative at a point means having a second-order Taylor expansion at that point with a local error smaller than any quadratic.
The result is closely related to Rademacher's theorem.
==References==

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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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