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.
Funder
Consejería de Economía, Conocimiento, Empresas y Universidad
Ministerio de Ciencia, Innovación y Universidades
Regional Government of Andalusia
Department of Mathematics of the University of Cadiz
aid program for the requalification of the Spanish University System of the Spanish Ministry of Universities and the European Union-Next GenerationEU
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
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