On representations of functions from [0, 1] to [0, 1] by random equimeasured subsets
Résumé
Given a measurable function $u$ from [0, 1] to [0, 1], a random Borelian subset $E $of [0, 1] is constructed, so that (i) the Lebesgue measure of E is constant and (ii) for any $t$ from [0, 1], the probability that $t$ belongs to E is given by $u(t)$. An application to the existence of a random bang-bang controller in optimal control is given.
Domaines
Probabilités [math.PR]| Origine | Fichiers produits par l'(les) auteur(s) |
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