Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Keywords

  • Conditional expectation
  • Lyapunov convexity theorem
  • Young measures
  • bang-bang principle
  • purification principle

Mathematics Subject Classification

28B05, 46G10, 46N10

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Suggested citation

Y. Askoura, M. Sbihi. “A Bang-Bang Principle for the Conditional Expectation Vector Measure.” Journal of Convex Analysis 33 (2026), No. 1&2, 377–392. https://doi.org/10.68381/jca33023

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Published by Heldermann Verlag, 2026. Rights now held by Banach Press LLC.