XI: 05, 47-50, LNM 581 (1977)
DELLACHERIE, Claude
Deux remarques sur la séparabilité optionnelle (
General theory of processes)
Optional separability was defined by Doob,
Ann. Inst. Fourier, 25, 1975. See also Benveniste,
1025. The main remark in this paper is the following: given any optional set $H$ with countable dense sections, there exists a continuous change of time $(T_t)$ indexed by $[0,1[$ such that $H$ is the union of all graphs $T_t$ for $t$ dyadic. Thus Doob's theorem amounts to the fact that every optional process becomes separable in the ordinary sense once a suitable continuous change of time has been performed
Keywords: Optional processes,
Separability,
Changes of timeNature: Original
Retrieve article from Numdam
