8.1 A measure defined on a semiring Φ is said to be strictly regular if its main prolongation is a prolongation of a Radon measure. If each open subset of Ω is a countable union of compact sets, if Φ̃ is the Borel σ-algebra, and if each compact set is μ-integrable, then μ is strictly regular (Theorem 8.1.2).
KeywordsOpen Subset Lebesgue Measure Radon Measure Countable Union Compact Hausdorff Space
Unable to display preview. Download preview PDF.