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In mathematics, Kōmura's theorem is a result on the differentiability of absolutely continuous Banach space-valued functions, and is a substantial generalization of Lebesgue's theorem on the differentiability of the indefinite integral, which is that Φ : () → R given by : is differentiable at ''t'' for almost every 0 < ''t'' < ''T'' when ''φ'' : () → R lies in the ''L''''p'' space ''L''1((); R). ==Statement of the theorem== Let (''X'', || ||) be a reflexive Banach space and let ''φ'' : () → ''X'' be absolutely continuous. Then ''φ'' is (strongly) differentiable almost everywhere, the derivative ''φ''′ lies in the Bochner space ''L''1((); ''X''), and, for all 0 ≤ ''t'' ≤ ''T'', : 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Kōmura's theorem」の詳細全文を読む スポンサード リンク
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