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Regular measure

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A measure defined on the Borel -algebra of a topological space such that for any Borel set and any there is an open set containing , , and such that . An equivalent definition is as follows: For any and any there is a closed set such that .


Comments

See also Regular set function.

This notion of regular measure should not be confused with that of a regular outer measure, which is an outer measure (cf. also Measure) such that for every there is a measurable set such that .

References

[a1] M.E. Munroe, "Introduction to measure and integration" , Addison-Wesley (1953) pp. 111
How to Cite This Entry:
Regular measure. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Regular_measure&oldid=27568
This article was adapted from an original article by R.A. Minlos (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article