12. Perimeter measurements
The term perimeter refers strictly to the length of a differentiable Jordan curve of class C1 (or even Lipchitzian), or more generally to the "area" of a (n - 1)-dimensional simple closed hyper-surface of class C1 (or even Lipchitzian), and largo sensu to the "size" of the boundary of a subset of .
There are several notions of perimeter.
The (n - 1)-dimensional Hausdorff measure, denoted ,...
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Perimeter measurements
Bibliography
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(1) - ALBERTI (G.) - Geometric measure theory. - Encyclopedia of Mathematical Physics, Vol. 2, pp. 520-527 (J.-P. Françoise et al, eds), Elsevier (2006).
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(2) - AMBROSIO (L.), CAPASSO (V.), VILLA (E.) - On the approximation of mean densities of random closed sets. - Bernoulli,...
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