regular Borel measure

regular Borel measure

[′reg·yə·lər bə′rel ‚mezh·ər]
(mathematics)
A Borel measure such that the measure of any Borel set E is equal to both the greatest lower bound of measures of open Borel sets containing E, and to the least upper bound of measures of compact sets contained in E. Also known as Radon measure.
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Our proof is obtained by the regularity properties of the corresponding regular Borel measure on [?
Considering [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], we shall get an E-valued regular Borel measure [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] ([7]) (we denote the measure j by the same notation as operator [?
In this case we prove that any Baire measure can be uniquely extended to regular Borel measure.