On the equivalence of Aumann and Herer expectations of random sets

• Autores: Pedro Nicolás Terán Agraz
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 17, Nº. 3, 2008, págs. 505-514
• Idioma: inglés
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• Resumen

  • Spaces where the Aumann and Herer notions of expectation of a random set coincide are exactly those having the Mazur Intersection Property (the closed convex hull of a bounded set is the intersection of all balls covering it). For a random compact set, more can be said: its Herer expectation is always the intersection of all closed balls covering its Aumann expectation. Some further consequences of these results are presented.