\begin{definition}[Definition:Infinite Measure]
Let $\struct {X, \Sigma}$ be a measurable space.
Then the '''infinite measure''' is the measure defined by:
:$\mu: \Sigma \to \overline \R, \ \map \mu E := \begin{cases} 0 & : \text{if } E = \O \\ +\infty & : \text{otherwise}\end{cases}$
where $\overline \R$ denotes the extended real numbers.
\end{definition}