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
The null measure 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
- Results about the null measure can be found here.
Sources
- 2005: René L. Schilling: Measures, Integrals and Martingales ... (previous) ... (next): $4.7 \ \text{(v)}$
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): null measure
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): zero measure