  This paper shows that finitely additive measures occur naturally in very
general Divergence Theorems. The main results are two such theorems. The first
proves the existence of pure normal measures for sets of finite perime- ter,
which yield a Gau{\ss} formula for essentially bounded vector fields having
divergence measure. The second extends a result of Silhavy [19] on normal
traces. In particular, it is shown that a Gau{\ss} Theorem for unbounded vector
fields having divergence measure necessitates the use of pure measures acting
on the gradient of the scalar field. All of these measures are shown to have
their core on the boundary of the domain of integration.
