8. The n-dimensional Lebesgue measure

8.1 Definition

Definition (Lebesgue measure) (1901). The n-dimensional Lebesgue measure, denoted $μ_{L_{n}}$ , is the only measure in $ℝ^{n}$ , regular borelian, and invariant by translation, such that the measure of the unit cube [0, 1] ⁿ is 1 (

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The n-dimensional Lebesgue measure

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Bibliography

(1) - ALBERTI (G.) - Geometric measure theory. - Encyclopedia of Mathematical Physics, Vol. 2, pp. 520-527 (J.-P. Françoise et al, eds), Elsevier (2006).
(2) - AMBROSIO (L.), CAPASSO (V.), VILLA (E.) - On the approximation of mean densities of random closed...

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