Pure Measures, Traces and a General Theorem of Gauß

In this thesis, the structure of pure measures is investigated. These are elements of the dual of the space of essentially bounded functions. A more precise representation of the dual space of the space of essentially bounded functions is given, leading to the definition and analysis of density measurs which constitute a new large class and yield numerous new examples of pure measures which are well-suited for applications in very general Divergence Theorems. The existence of pure normal measures for sets of finite perimeter is demonstrated. These yield Gauß formulas for essentially bounded vector fields having divergence measure. Furthermore, a result of Silhavy is extended. In particular, it is shown that a Gauß-Green Theorem for unbounded vector fields having divergence measure necessitates the use of pure measures acting on the gradient of the scalar field