Definition:Null Measure

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

Then the null measure is the measure defined by:


 * $\mu: \Sigma \to \overline \R: \map \mu E := 0$

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.

Some sources give this as zero measure.

Also see

 * Null Measure is Measure
 * Definition:Infinite Measure