Measure theory MOC

Regular measure

Let be a topological space and a measure space . Let denote the set of all compact subsets of . A measurable set is said to be inner regular iff

and outer regular iff

A measure is called inner regular iff every measurable set is inner regular, and likewise a measure is called outer regular iff every measurable set is outer regular. A measure which is both inner regular and outer regular is called regular. measure Thus a measure is regular iff

for every .

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