Lebesgue integral

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Named after Henri Lebesgue, a French mathematician.


  • (US) IPA(key): /ləˈbɛːɡ ˈɪntəɡɹəl/, /ləˈbɛːɡ ˈɪntəɡɹl̩/


Lebesgue integral (plural Lebesgue integrals)

  1. (analysis, singular only, definite and countable) 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. (Formal definitions can be found at PlanetMath).
    The Lebesgue integral is learned in a first-year real-analysis course.
    Compute the Lebesgue integral of f over E.