# 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.