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The one-way Fubini property and conditional independence : an equivalence result
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Hammond, Peter J. and Sun, Yeneng (2021) The one-way Fubini property and conditional independence : an equivalence result. Advances in Mathematics, 376 . 107487. doi:10.1016/j.aim.2020.107487 ISSN 0001-8708.
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Official URL: https://doi.org/10.1016/j.aim.2020.107487
Abstract
A process defined by a continuum of random variables with non-degenerate idiosyncratic risk is not jointly measurable with respect to the usual product σ-algebra. We show that the process is jointly measurable in a one-way Fubini extension of the product space if and only if there is a countably generated σ-algebra given which the random variables are essentially pairwise conditionally independent, while their conditional distributions also satisfy a suitable joint measurability condition. Applications include: (i) new characterizations of essential pairwise independence and essential pairwise exchangeability; (ii) when a one-way Fubini extension exists, the need for the sample space to be saturated if there is an essentially random regular conditional distribution with respect to the usual product σ-algebra.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Social Sciences > Economics | ||||||||
Journal or Publication Title: | Advances in Mathematics | ||||||||
Publisher: | Academic Press | ||||||||
ISSN: | 0001-8708 | ||||||||
Official Date: | 6 January 2021 | ||||||||
Dates: |
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Volume: | 376 | ||||||||
Article Number: | 107487 | ||||||||
DOI: | 10.1016/j.aim.2020.107487 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 27 October 2020 | ||||||||
Date of first compliant Open Access: | 23 November 2020 | ||||||||
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