Let $v : \mathcal {P}(\mathbb R) \to [0,\infty]$ a set-function such that $\displaystyle{ v(F \cup E) \leq v(E) + v(F) \quad \forall E,F \subset \mathbb R}$.
Is always true that: $ \displaystyle{ v\left(\bigcup_{n=1}^{\infty} A_n\right) \leq \sum_{n=1}^{\infty} v(A_n)}$ ?
I think this is not but I can't find a counterexample. Any help?
Thank's in advance!