Perimeter measurements
Geometric Measure Theory

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 ${ℝ}^n$ .

There are several notions of perimeter.