On Focal Borel Probability Measures

Francisco Javier García-Pacheco (), Jorge Rivero-Dones and Moisés Villegas-Vallecillos
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Francisco Javier García-Pacheco: Department of Mathematics, College of Engineering, University of Cádiz, 11003 Cádiz, Spain
Jorge Rivero-Dones: Department of Mathematics, Faculty of Sciences, University of Cádiz, 11003 Cádiz, Spain
Moisés Villegas-Vallecillos: Department of Mathematics, College of Naval Engineering, University of Cádiz, 11003 Cádiz, Spain

Mathematics, 2022, vol. 10, issue 22, 1-13

Abstract: The novel concept of focality is introduced for Borel probability measures on compact Hausdorff topological spaces. We characterize focal Borel probability measures as those Borel probability measures that are strictly positive on every nonempty open subset. We also prove the existence of focal Borel probability measures on compact metric spaces. Lastly, we prove that the set of focal (regular) Borel probability measures is convex but not extremal in the set of all (regular) Borel probability measures.

Keywords: borel ? -algebra; probability measure; compact Hausdorff topological space; compact metric space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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