Journal of Convex Analysis 33 (2026), No. 1&2, 377--392
Copyright Heldermann Verlag 2026
A Bang-Bang Principle for the Conditional Expectation Vector Measure
Youcef Askoura
LEMMA, Université Paris-Panthéon-Assas, Paris, France
youcef.askoura@u-paris2.fr
Mohammed Sbihi
ENAC, Université de Toulouse, Toulouse, France
mohammed.sbihi@enac.fr
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.
Keywords: Conditional expectation, Lyapunov convexity theorem, Young measures, bang-bang principle, purification principle.
MSC: 28B05, 46G10, 46N10.
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