Definition:Strongly Additive Function

Definition

Let $\SS$ be an algebra of sets.

Let $f: \SS \to \overline \R$ 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:

$\forall S, T \in \SS: \map f {S \cup T} + \map f {S \cap T} = \map f S + \map f T$

Examples

• Additive Function is Strongly Additive
• Measure is Strongly Additive