Please use this identifier to cite or link to this item: https://doi.org/10.1090/S0002-9939-05-08016-0
Title: Joint measurability and the one-way Fubini property for a continuum of independent random variables
Authors: Hammond, P.J.
Sun, Y. 
Keywords: Continuum of independent random variables
Joint measurability problem
Loeb product measures
One-way Fubini property
Product-measurable sets
Issue Date: Mar-2006
Citation: Hammond, P.J., Sun, Y. (2006-03). Joint measurability and the one-way Fubini property for a continuum of independent random variables. Proceedings of the American Mathematical Society 134 (3) : 737-747. ScholarBank@NUS Repository. https://doi.org/10.1090/S0002-9939-05-08016-0
Abstract: As is well known, a continuous parameter process with mutually independent random variables is not jointly measurable in the usual sense. This paper proposes an extension of the usual product measure-theoretic framework, using a natural "one-way Fubini" property. When the random variables are independent even in a very weak sense, this property guarantees joint measurability and defines a unique measure on a suitable minimal σr-algebra. However, a further extension to satisfy the usual (two-way) Fubini property, as in the case of Loeb product measures, may not be possible in general. Some applications are also given. © 2005 American Mathematical Society.
Source Title: Proceedings of the American Mathematical Society
URI: http://scholarbank.nus.edu.sg/handle/10635/103457
ISSN: 00029939
DOI: 10.1090/S0002-9939-05-08016-0
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