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XV: 36, 529-546, LNM 850 (1981)
JACOD, Jean; MÉMIN, Jean
Sur un type de convergence intermédiaire entre la convergence en loi et la convergence en probabilité (Measure theory)
For simplicity we consider only real valued r.v.'s, but it is essential that the paper considers general Polish spaces instead of $R$. Let us define a fuzzy r.v. $X$ on $(\Omega, {\cal F},P)$ as a probability measure on $\Omega\timesR$ whose projection on $\Omega$ is $P$. In particular, a standard r.v. $X$ defines such a measure as the image of $P$ under the map $\omega\mapsto (\omega,X(\omega))$. The space of fuzzy r.v.'s is provided with a weak topology, associated with the bounded functions $f(\omega,x)$ which are continuous in $x$ for every $\omega$, or equivalently with the functions $I_A(\omega)\,f(x)$ with $f$ bounded continuous. The main topic of this paper is the study of this topology
Comment: From this description, it is clear that this paper extends to general Polish spaces the topology of Baxter-Chacon (forgetting about the filtration), for which see 1228
Keywords: Fuzzy random variables, Convergence in law
Nature: Original
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