Regularity of Riesz Measures

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Feb 1986Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 96, page 330 (issn: 0002-9939,

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Authors: Prinz, P.;

doi: 10.2307/2046176 , 10.1090/s0002-9939-1986-0818467-6

Regularity of Riesz Measures

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Abstract

It is shown that Riesz measures are inner regular, i.e., each Borel set may be approximated from inside by closed sets, if the basic space is metacompact or para-Lindelöf. On the other hand, an example is given to show that local compactness is not sufficient to ensure inner regularity of Riesz measures.

Keywords

Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties), Riesz measure, concassage of Radon measure, Local compactness, \(\sigma\)-compactness, Hausdorff topological space, Noncompact covering properties (paracompact, Lindelöf, etc.), Set functions and measures on topological spaces (regularity of measures, etc.), inner regular measure, metacompact, para-Lindelöf

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