Lebesgue measure

English

Etymology

Named after French mathematician Henri Lebesgue.

Pronunciation

(US) IPA^(key): /ləˈbɛːɡ ˈmɛ.ʒɚ/

Noun

Lebesgue measure (plural Lebesgue measures)

(mathematical analysis) 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).

Hypernyms

complete measure < positive measure < measure

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