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Transverse measure : ウィキペディア英語版 | Transverse measure In mathematics, a measure on a real vector space is said to be transverse to a given set if it assigns measure zero to every translate of that set, while assigning finite and positive (i.e. non-zero) measure to some compact set. ==Definition==
Let ''V'' be a real vector space together with a metric space structure with respect to which it is a complete space. A Borel measure ''μ'' is said to be transverse to a Borel-measurable subset ''S'' of ''V'' if * there exists a compact subset ''K'' of ''V'' with 0 < ''μ''(''K'') < +∞; and * ''μ''(''v'' + ''S'') = 0 for all ''v'' ∈ ''V'', where :: :is the translate of ''S'' by ''v''. The first requirement ensures that, for example, the trivial measure is not considered to be a transverse measure.
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「Transverse measure」の詳細全文を読む
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