Axiom:Measure Axioms

Definition
Let $\struct {X, \Sigma}$ be a measurable space.

Let $\mu: \Sigma \to \overline \R$ be a mapping, where $\overline \R$ denotes the set of extended real numbers.

Then $\mu$ is called a measure on $\Sigma$ $\mu$ fulfils either of the following axiom schemata: