%0 Unpublished work %T A bang-bang principle for the conditional expectation vector measure %+ LEMMA, Université Paris II %+ ENAC - Equipe Optim (OPTIM) %A Askoura, Youcef %A Sbihi, Mohammed %8 2022-02-01 %D 2022 %Z 2201.13196 %R 10.48550/ARXIV.2201.13196 %K onditional expectation %K Lyapunov convexity theorem %K Young measures %K Bang- bang principle %K purification principle %Z 28B05, 46G10, 46N10 %Z Mathematics [math]Preprints, Working Papers, ... %X We 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. %G English %L hal-03945255 %U https://enac.hal.science/hal-03945255 %~ ENAC %~ INSMI %~ OPTIM