Definition:Infinite Measure

Definition
Let $\left({X, \mathcal A}\right)$ be a measurable space.

Then the infinite measure is the measure defined by:


 * $\mu: \mathcal A \to \overline{\R}, \ \mu \left({A}\right) = \begin{cases}0 & \text{if $A = \varnothing$} \\ +\infty & \text{otherwise}\end{cases}$

where $\overline{\R}$ denotes the extended real numbers.

Also known as
This may be referred to as the trivial measure, but such can cause confusion with the null measure.

Also see

 * Infinite Measure is Measure
 * Null Measure