Definition:Null Measure

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

Then the null measure is the measure defined by:


 * $\mu: \Sigma \to \overline{\R}, \ \mu \left({E}\right) := 0$

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 infinite measure.

Also see

 * Null Measure is Measure
 * Infinite Measure