%0 Unpublished work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