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On Focal Borel Probability Measures

Author

Listed:
  • Francisco Javier García-Pacheco

    (Department of Mathematics, College of Engineering, University of Cádiz, 11003 Cádiz, Spain
    These authors contributed equally to this work.)

  • Jorge Rivero-Dones

    (Department of Mathematics, Faculty of Sciences, University of Cádiz, 11003 Cádiz, Spain
    These authors contributed equally to this work.)

  • Moisés Villegas-Vallecillos

    (Department of Mathematics, College of Naval Engineering, University of Cádiz, 11003 Cádiz, Spain
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Francisco Javier García-Pacheco & Jorge Rivero-Dones & Moisés Villegas-Vallecillos, 2022. "On Focal Borel Probability Measures," Mathematics, MDPI, vol. 10(22), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4365-:d:978417
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