https://enac.hal.science/hal-03945255Askoura, YoucefYoucefAskouraLEMMA, Université Paris IISbihi, MohammedMohammedSbihiOPTIM - ENAC - Equipe Optim - ENAC - Ecole Nationale de l'Aviation CivileA bang-bang principle for the conditional expectation vector measureHAL CCSD2022onditional expectationLyapunov convexity theoremYoung measuresBang- bang principlepurification principle[MATH] Mathematics [math]Sbihi, Mohammed2023-01-18 14:59:242023-01-31 11:27:092023-01-18 14:59:24enPreprints, Working Papers, ...10.48550/ARXIV.2201.131961We prove a conditional expectation bang-bang principle. Based on properties of the conditional expectation vector measure, we establish that the conditional expectation of a set-valued mapping coincides with the conditional expectation of the set of selections of its extreme points part. As a by-product, we obtain straightforwardly a purification principle.