Definition:Null Measure

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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


Sources