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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 Fine topology (potential theory) ： ウィキペディア英語版 Fine topology (potential theory) In mathematics, in the field of potential theory, the fine topology is a natural topology for setting the study of subharmonic functions. In the earliest studies of subharmonic functions, namely those for which $\backslash Delta\; u\; \backslash ge\; 0,$ where $\backslash Delta$ is the Laplacian, only smooth functions were considered. In that case it was natural to consider only the Euclidean topology, but with the advent of upper semi-continuous subharmonic functions introduced by F. Riesz, the fine topology became the more natural tool in many situations. == Definition == The fine topology on the Euclidean space $\backslash R^n$ is defined to be the coarsest topology making all subharmonic functions (equivalently all superharmonic functions) continuous. Concepts in the fine topology are normally prefixed with the word 'fine' to distinguish them from the corresponding concepts in the usual topology, as for example 'fine neighbourhood' or 'fine continuous'. 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「Fine topology (potential theory)」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.