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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 Cramér–Wold theorem ： ウィキペディア英語版 Cramér–Wold theorem In mathematics, the Cramér–Wold theorem in measure theory states that a Borel probability measure on $R^k$ is uniquely determined by the totality of its one-dimensional projections. It is used as a method for proving joint convergence results. The theorem is named after Harald Cramér and Herman Ole Andreas Wold. Let :$\backslash overline\_n\; =\; (X\_,\backslash dots,X\_)\; \backslash ;$ and :$\backslash ;\; \backslash overline\; =\; (X\_1,\backslash dots,X\_k)$ be random vectors of dimension ''k''. Then $\backslash overline\_n$ converges in distribution to $\backslash overline$ if and only if: :$\backslash sum\_^k\; t\_iX\_\; \backslash overset\}\; \backslash sum\_^k\; t\_iX\_i.$ for each $(t\_1,\backslash dots,t\_k)\backslash in\; \backslash mathbb^k$, that is, if every fixed linear combination of the coordinates of $\backslash overline\_n$ converges in distribution to the correspondent linear combination of coordinates of $\backslash overline$. ==Proof== For a proof, see for example 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「Cramér–Wold 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.