Functions of bounded variation in one and multiple dimensions

In this Masters thesis, we investigate the properties of functions of bounded variation. First, we consider univariate functions, afterwards we generalize this notion to higher dimensions. There are many different definitions of multivariate functions of bounded variation. We study functions of bounded variation in the senses of Vitali; Hardy and Krause; Arzelà; and Hahn. Many results for those functions of bounded variation were previously only known in the bivariate case. We extend them to arbitrary dimensions, and also add some new results.