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

Herer, Wojciech

C. R. Acad. Sci., Paris, Sér. I 302, 131-134 (1986).

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

Citations:

Zbl 0033.28902