The One-way Fubini Property and Conditional Independence: An Equivalence Result

Peter Hammond and Yeneng Sun
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Yeneng Sun: Department of Mathematics, National University of Singapore

CRETA Online Discussion Paper Series from Centre for Research in Economic Theory and its Applications CRETA

Abstract: A general parameter process defined by a continuum of random variables is not jointly measurable with respect to the usual product sigma-algebra. For the case of independent random variables, a one-way Fubini extension of the product space was constructed in our 2006 paper (“Joint measurability and the one-way Fubini property for a continuum of independent random variables”, Proceedings of the American Mathematical Society, 134: 737–747) to satisfy a limited form of joint measurability. For the general case we show that this extension exists if and only if there is a countably generated sigma-algebra given which the random variables are essentially pairwise conditionally independent, while their joint conditional distribution also satisfies a suitable joint measurability condition. Applications include new characterizations of essential pairwise independence and essential pairwise exchangeability through regular conditional distributions with respect to the usual product sigma-algebra in the framework of a one-way Fubini extension.

Keywords: Continuum of random variables; joint measurability problem; one-way Fubini property; conditional distributions; characterizations of conditional independence (search for similar items in EconPapers)
Date: 2016
New Economics Papers: this item is included in nep-sea
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Citations: View citations in EconPapers (2)

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