Pré-Publication, Document De Travail Année : 2025

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.

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Dates et versions

hal-04896256 , version 1 (19-01-2025)

Identifiants

  • HAL Id : hal-04896256 , version 1

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Laurent Miclo. On representations of functions from [0, 1] to [0, 1] by random equimeasured subsets. 2025. ⟨hal-04896256⟩
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