Caccioppoli set

Summary

A Caccioppoli set, or set of finite perimeter, is a measurable subset of $\R^n$ whose perimeter is finite. Equivalently, its indicator function has bounded variation. These sets are the measure-theoretic replacement for regions with smooth boundary. They are closed under the limits that appear when one minimizes area. So they give a setting where problems such as the isoperimetric problem have solutions.