An overview on B V Functions and Sets of Finite Perimeter in Rn

The aim of the thesis is to carry out an analysis on two topics: functions of bounded variation (which are L^1 functions defined on an open set of R^n whose distributional derivative is a Radon measure), and sets of finite perimeter in R^n (L^n measurable sets whose characteristic function belongs to the space B V). After considering some measure theory preliminary results, B V functions are defined and studied through the notion of variation, then the exposition narrows down just to B V functions of one variable and their properties. Finally, sets of finite perimeter are considered, together with related concepts such as Coarea Formula for B V functions, Isoperimetric Inequalities and the reduced boundary of a set