# Definition:Null Measure

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## Contents

## 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

- 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): Entry:**zero measure**