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Sur la séparabilité et la continuité des functions alétoires. (French) Zbl 0666.60038
We study the processes which has a given separating set, S (in Doob’s theory). The set of theirs laws is an extremal set of measures. We show, with the help of an almost sure continuity hypothesis, that the law of the process is determined by its projection on S. With only the hypothesis of continuity in probability, the projection on S of the law of the process has a property of extremality.
MSC:
60G05 Foundations of stochastic processes
60G07 General theory of stochastic processes
28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
28A35 Measures and integrals in product spaces
28A60 Measures on Boolean rings, measure algebras
44A55 Discrete operational calculus
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