XII: 39, 512-514, LNM 649 (1978)
DELLACHERIE, Claude
Sur l'existence de certains ess.inf et ess.sup de familles de processus mesurables (General theory of processes)
The word ``essential'' in the title refers to inequalities between processes up to evanescent sets. Since in the case of a probability space consisting of one point, this means inequalities everywhere, it is clear that additional assumptions are necessary. Such essential bounds are shown to exist whenever the sample functions are upper semicontinuous in the right topology, or the left topology (and of course also if they are lower semicontinuous). This covers in particular the case of strong supermartingales and Snell's envelopes
Keywords: Essential suprema, Evanescent sets
Nature: Original
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