翻訳と辞書
Words near each other
・ Numancia, Aklan
・ Numangatini Tione Ariki
・ Numanggang language
・ Numanlar, Kastamonu
・ Numanohata Station
・ Numanosawa Station
・ Null modem
・ Null morpheme
・ Null move
・ Null Object pattern
・ Null pointer
・ Null result
・ Null route
・ Null semigroup
・ Null session
Null set
・ Null sign
・ Null Stern Hotel
・ Null Subject Parameter
・ Null symbol
・ Null vector
・ Null vector (disambiguation)
・ Null-A Three
・ Null-move heuristic
・ Null-O
・ Null-subject language
・ Null-terminated string
・ Nulla bona
・ Nulla in mundo pax sincera
・ Nulla poena pro vitium Abyssus


Dictionary Lists
翻訳と辞書 辞書検索 [ 開発暫定版 ]
スポンサード リンク

Null set : ウィキペディア英語版
Null set

In set theory, a null set ''N'' ⊂ R is a set that can be covered by an countable union of intervals of arbitrarily small total length. The notion of null set in set theory anticipates the development of Lebesgue measure since a null set necessarily has measure zero.
== Definition ==
Suppose ''A'' is a subset of the real line R such that
:\forall \epsilon > 0 \ \exists \ (A \subset \bigcup_1 ^\infty U_n \ \and \ \sum_1^\infty |U_n| < \epsilon )
where the ''U''n are intervals and |''U''| is the length of ''U'', then ''A'' is a null set.〔John Franks (2009) A (Terse) ''Introduction to Lebesgue Integration'', page 28, American Mathematical Society ISBN 978-0-8218-4862-3 〕
In terminology of mathematical analysis, this definition requires that there be a sequence of open covers of ''A'' for which the limit of the lengths of the covers is zero.
Null sets include all finite sets, all countable sets, and even some uncountable sets such as the Cantor set.

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「Null set」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.