# Lebesgue measure

## English

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### Pronunciation

• (US) IPA(key): /ləˈbɛːg ˈmɛ.ʒɚ/

### Noun

Lebesgue measure (plural Lebesgue measures)

1. (analysis) (For a given k-dimensional Euclidean space,) the unique complete translation-invariant measure for the σ-algebra which contains all k-cells in $\mathbb{R}^k$ 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).