HAL CCSD
A bang-bang principle for the conditional expectation vector measure
Askoura, Youcef
Sbihi, Mohammed
LEMMA, Université Paris II
ENAC - Equipe Optim (OPTIM) ; Ecole Nationale de l'Aviation Civile (ENAC)
hal-03945255
https://enac.hal.science/hal-03945255
https://enac.hal.science/hal-03945255
2022
ARXIV: 2201.13196
info:eu-repo/semantics/altIdentifier/arxiv/2201.13196
DOI: 10.48550/ARXIV.2201.13196
info:eu-repo/semantics/altIdentifier/doi/10.48550/ARXIV.2201.13196
en
onditional expectation
Lyapunov convexity theorem
Young measures
Bang- bang principle
purification principle
28B05, 46G10, 46N10
[MATH]Mathematics [math]
info:eu-repo/semantics/preprint
Preprints, Working Papers, ...
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.
2022-02-01