## Mathematical expectation in the sense of Doss of a random variable with values in a metric space. (Espérance mathématique au sens de Doss d’une variable aléatoire à valeurs dans un espace métrique.)(French)Zbl 0609.60002

Let $$f$$ be a random variable with values in a metric space $$X$$. We define (developing an idea of S. Doss [Bull. Sci. Math., II. Ser. 73, 1–26 (1949; Zbl 0033.28902)]) mathematical expectation of $$f$$ as a closed, bounded, non empty subset of $$X$$ and conditional expectation of $$f$$ with respect to a $$\sigma$$-algebra as a random set.
Reviewer: Wojciech Herer

### MSC:

 60B05 Probability measures on topological spaces

### Keywords:

conditional expectation; random set

Zbl 0033.28902