  Necessary and sufficient conditions for weak and vague convergence of
measures are important for a diverse host of applications. This paper aims to
give a comprehensive description of the relationship between the two modes of
convergence when the measures are signed, which is largely absent from the
literature. Furthermore, when the underlying space is $\mathbb{R}$, we study
the relationship between vague convergence of signed measures and the pointwise
convergence of their distribution functions.
