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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 Lelong number ： ウィキペディア英語版 Lelong number In mathematics, the Lelong number is an invariant of a point of a complex analytic variety that in some sense measures the local density at that point. It was introduced by . More generally a closed positive (''p'',''p'') current ''u'' on a complex manifold has a Lelong number ''n''(''u'',''x'') for each point ''x'' of the manifold. Similarly a plurisubharmonic function also has a Lelong number at a point. ==Definitions== The Lelong number of a plurisubharmonic function φ at a point ''x'' of C''n'' is :$\backslash liminf\_\backslash frac.$ For a point ''x'' of an analytic subset ''A'' of pure dimension ''k'', the Lelong number ν(''A'',''x'') is the limit of the ratio of the areas of ''A'' ∩ ''B''(''r'',''x'') and a ball of radius ''r'' in C''k'' as the radius tends to zero. (Here ''B''(''r'',''x'') is a ball of radius ''r'' centered at ''x''.) In other words the Lelong number is a sort of measure of the local density of ''A'' near ''x''. If ''x'' is not in the subvariety ''A'' the Lelong number is 0, and if ''x'' is a regular point the Lelong number is 1. Thie proved that the Lelong number ν(''A'',''x'') is always an integer. 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「Lelong number」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.