Lebesgue measure

noun

A unique complete translation-invariant measure for the σ-algebra which contains all k-cells in a given Euclidean space, and which assigns a measure to each k-cell which is equal to that k-cell's volume (as defined in Euclidean geometry: i.e., the volume of the k-cell equals the product of the lengths of its sides).

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Meanings

nounLebesgue measure (plural Lebesgue measures)

plural Lebesgue measures

  1. mathematical analysisA unique complete translation-invariant measure for the σ-algebra which contains all k-cells in a given Euclidean space, and which assigns a measure to each k-cell which is equal to that k-cell's volume (as defined in Euclidean geometry: i.e., the volume of the k-cell equals the product of the lengths of its sides).

Origin

Named after French mathematician Henri Lebesgue.

Full word history & related roots →

Translations

Bulgarian Лебегова мярка
  • Лебегова мярка (Lebegova mjarka)Translations
German Lebesgue-Maß
  • Lebesgue-MaßTranslations
Polish miara Lebesgue'a
  • miara Lebesgue'aTranslations
Cite this entry
APA

Lebesgue measure. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Lebesgue%20measure

MLA

“Lebesgue measure.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Lebesgue%20measure. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Lebesgue measure,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Lebesgue%20measure.

Source: Lebesgue measure on Wiktionary, CC BY-SA 4.0.