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}
}
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17 pages