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12. Perimeter measurements
The term perimeter refers strictly to the length of a differentiable Jordan curve of class C 1 (or even Lipchitzian), or more generally to the "area" of a (n - 1)-dimensional simple closed hyper-surface of class C 1 (or even Lipchitzian), and largo sensu to the "size" of the boundary of a subset of .
There are several notions of perimeter.
12.1 The (n - 1)-dimensional Hausdorff measure
The (n - 1)-dimensional Hausdorff measure, denoted
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Perimeter measurements
Invariant measurements
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