Helly's selection theorem

英語（米国） (en-US) 英語（イギリス） (en-GB)

固有名詞

(mathematics) A theorem stating that a sequence of functions that is locally of bounded total variation and uniformly bounded at a point has a convergent subsequence.

日本語の意味

ヘリーの選択定理：局所的に全変動が有界で、かつある一点で一様に有界な関数列は、収束する部分列を持つという数学上の定理

英語の意味

(mathematics) A theorem stating that a sequence of functions that is locally of bounded total variation and uniformly bounded at a point has a convergent subsequence.

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In our analysis seminar, we proved Helly's selection theorem and then used it to extract a convergent subsequence from a family of functions that are locally of bounded total variation and uniformly bounded at a point.

解析セミナーで、局所的に総変動が有界でありある点で一様に有界な関数列は収束部分列を持つという定理を証明し、その定理を用いてそのような関数族から収束部分列を取り出しました。

詳細

意味（1）

(mathematics) A theorem stating that a sequence of functions that is locally of bounded total variation and uniformly bounded at a point has a convergent subsequence.