English

A bang-bang principle for the conditional expectation vector measure

Functional Analysis 2022-02-01 v1

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.

Cite

@article{arxiv.2201.13196,
  title  = {A bang-bang principle for the conditional expectation vector measure},
  author = {Youcef Askoura and Mohammed Sbihi},
  journal= {arXiv preprint arXiv:2201.13196},
  year   = {2022}
}

Comments

17 pages

R2 v1 2026-06-24T09:10:39.955Z