Lebesgue integral

noun

An integral which has more general application than that of the Riemann integral, because it allows the region of integration to be partitioned into not just intervals but any measurable sets for which the function to be integrated has a sufficiently narrow range.

“Compute the Lebesgue integral of f over E.”

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Meanings

nounLebesgue integral (plural Lebesgue integrals)

plural Lebesgue integrals

  1. singularsingular onlymathematical analysisAn integral which has more general application than that of the Riemann integral, because it allows the region of integration to be partitioned into not just intervals but any measurable sets for which the function to be integrated has a sufficiently narrow range.

    The Lebesgue integral is learned in a first-year real-analysis course.

  2. singularsingular onlymathematical analysisThe result of the application of the Lebesgue integral

    Compute the Lebesgue integral of f over E.

Origin

Named after French mathematician Henri Lebesgue.

Full word history & related roots →

Translations

German Lebesgue-Integral
  • Lebesgue-IntegralTranslations
Polish całka Lebesgue'a
  • całka Lebesgue'aTranslations
Cite this entry
APA

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

MLA

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

Chicago

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

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