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On the equivalence of Aumann and Herer expectations of random sets

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Abstract

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.

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  1. Facultad de Ciencias Económicas y Empresariales, Unidad Docente de Métodos Estadísticos, Grupo Decisión Multicriterio Zaragoza, Universidad de Zaragoza, Gran Vía, 2, E-50005, Zaragoza, Spain

    Pedro Terán

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  1. Pedro Terán
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Terán, P. On the equivalence of Aumann and Herer expectations of random sets. TEST 17, 505–514 (2008). https://doi.org/10.1007/s11749-007-0043-0

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