7. Exterior measurements

The notion of external measure is a concept, due to C. Carathéodory (1918), which generalizes in an axiomatic framework a construction used preliminarily by H. Lebesgue (1902) to define the Lebesgue measure.

7.1 External measurement

Definition (outer measure) (Carathéodory, 1918). An exterior measure on $ℝ^{n}$ , denoted µ*, is a monotone, countably subadditive application defined on the collection $P (ℝ^{n})$ ...

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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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