Category:Finitely Additive Functions

This category contains results about Finitely Additive Functions.

Let $\SS$ be an algebra of sets.

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

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

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

That is, for any two disjoint elements of $\SS$, $f$ of their union equals the sum of $f$ of the individual elements.