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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 : 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
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