Definition:Diffuse Measure

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Definition

Let $\struct {X, \Sigma, \mu}$ be a measure space.

The measure $\mu$ is said to be diffuse if and only if there are no $\mu$-atoms.

Also known as

A diffuse measure is also known as:

a continuous measure

a non-atomic measure.

Also see

• Lebesgue Measure is Diffuse

• Results about diffuse measures can be found here.

Sources

• 2005: René L. Schilling: Measures, Integrals and Martingales ... (previous) ... (next): $\S 6$: Problem $5$