Definition
Let (X, T) be a topological space and let Σ be a σ-algebra on X. Let μ be a measure on (X, Σ). A measurable subset A of X is said to be inner regular if
and said to be outer regular if
- A measure is called inner regular if every measurable set is inner regular. Some authors use a different definition: a measure is called inner regular if every open measurable set is inner regular.
- A measure is called outer regular if every measurable set is outer regular.
- A measure is called regular if it is outer regular and inner regular.
Read more about this topic: Regular Measure
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