ABSTRACT
Our goal is to extend the divergence theorem from dyadic figures to more general sets, called the sets of finite perimeter. These sets have two equivalent definitions: geometric, which is intuitive but difficult to work with, and analytic, which is effective but nonintuitive. Both definitions are essential, as they complement each other. In this chapter, we introduce the geometric definition of perimeter, and derive elementary properties of sets whose perimeter is finite. Some of these properties will motivate the analytic concept of variation presented in the next chapter.
