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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 Montel's theorem ： ウィキペディア英語版 Montel's theorem In complex analysis, an area of mathematics, Montel's theorem refers to one of two theorems about families of holomorphic functions. These are named after Paul Montel, and give conditions under which a family of holomorphic functions is normal. ==Uniformly bounded families are normal== The first, and simpler, version of the theorem states that a uniformly bounded family of holomorphic functions defined on an open subset of the complex numbers is normal. This theorem has the following formally stronger corollary. Suppose that $\backslash mathcal$ is a family of meromorphic functions on an open set $D$. If $z\_0\backslash in\; D$ is such that $\backslash mathcal$ is not normal at $z\_0$, and $U\backslash subset\; D$ is a neighborhood of $z\_0$, then $\backslash bigcup\_\{f\backslash in\backslash mathcal\{F\}\}f(U)$ is dense in the complex plane. 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「Montel's 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.