Finite Signed Radon Measure on a Metric Space

In the setting of Radon Measures on Locally Compact Metric Spaces: Standing Notation, let $(X,d)$ be a metric space.

(i) Finite signed Radon measure. A finite signed Borel measure $\nu$ on $X$ is a finite signed Radon measure if its total variation $|\nu|$ (a finite Borel measure by Properties of the Total Variation: a Finite Measure, the Jordan Decomposition, Linear Combinations, the Total Variation Norm, and Integrability (i)) is a Radon measure.