Definition:Measure (Measure Theory)/Definition 1

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.

$\mu$ is called a measure on $\Sigma$ $\mu$ fulfils the following axioms:

Also see

 * Equivalence of Definitions of Measure (Measure Theory)