$. See Section \[subsec:esempi\] for a proof.  **0. The infinite variation, non-compactly supported case:** $\frac{d\nu_0}{d{\ensuremath{\textnormal{Leb}}}}(x)=x^{-0}{\ensuremath {\mathbb{I}}}_{{\ensuremath {\mathbb{R}}}_+}(x)$. 