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In probability theory, Lévy’s continuity theorem, named after the French mathematician Paul Lévy, connects convergence in distribution of the sequence of random variables with pointwise convergence of their characteristic functions. An alternative name sometimes used is Lévy’s convergence theorem.〔Williams (1991, section 18.1)〕 This theorem is the basis for one approach to prove the central limit theorem and it is one of the major theorems concerning characteristic functions. ==Theorem== Suppose we have If the sequence of characteristic functions converges pointwise to some function '''' : then the following statements become equivalent: 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「Lévy's continuity theorem」の詳細全文を読む スポンサード リンク
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