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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Denjoy–Young–Saks theorem ： ウィキペディア英語版 Denjoy–Young–Saks theorem In mathematics, the Denjoy–Young–Saks theorem gives some possibilities for the Dini derivatives of a function that hold almost everywhere. proved the theorem for continuous functions, extended it to measurable functions, and extended it to arbitrary functions. and give historical accounts of the theorem. ==Statement== If ''f'' is a real valued function defined on an interval, then outside a set of measure 0 the Dini derivatives of ''f'' satisfy one of the following four conditions at each point: *''f'' has a finite derivative *''D''+''f'' = ''D''–''f'' is finite, ''D''−''f'' = ∞, ''D''+''f'' = –∞. *''D''−''f'' = ''D''+''f'' is finite, ''D''+''f'' = ∞, ''D''–''f'' = –∞. *''D''−''f'' = ''D''+''f'' = ∞, ''D''–''f'' = ''D''+''f'' = –∞. 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「Denjoy–Young–Saks theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.