## Definition

Let $\mathcal S$ be an algebra of sets.

Let $f: \mathcal S \to \overline{\R}$ be a function, where $\overline{\R}$ denotes the extended set of real numbers.

Then $f$ is defined to be strongly additive if and only if:

$\forall S, T \in \mathcal S: f \left({S \cup T}\right) + f \left({S \cap T}\right) = f \left({S}\right) + f \left({T}\right)$