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In complex analysis, the analytic capacity of a compact subset ''K'' of the complex plane is a number that denotes "how big" a bounded analytic function from C \ ''K'' can become. Roughly speaking, γ(''K'') measures the size of the unit ball of the space of bounded analytic functions outside ''K''. It was first introduced by Ahlfors in the 1940s while studying the removability of singularities of bounded analytic functions. ==Definition== Let ''K'' ⊂ C be compact. Then its analytic capacity is defined to be : Here, denotes the set of bounded analytic functions ''U'' → C, whenever ''U'' is an open subset of the complex plane. Further, : : (note that usually ) 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「analytic capacity」の詳細全文を読む スポンサード リンク
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