Joint measurability and the oneway Fubini property for a continuum of independent random variables
Authors:
Peter J. Hammond and Yeneng Sun
Journal:
Proc. Amer. Math. Soc. 134 (2006), 737747
MSC (2000):
Primary 28A05, 60G07; Secondary 03E20, 03H05, 28A20
Published electronically:
July 18, 2005
MathSciNet review:
2180892
Fulltext PDF Free Access
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Additional Information
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 measuretheoretic framework, using a natural ``oneway 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 algebra. However, a further extension to satisfy the usual (twoway) Fubini property, as in the case of Loeb product measures, may not be possible in general. Some applications are also given.
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Additional Information
Peter J. Hammond
Affiliation:
Department of Economics, Stanford University, 579 Serra Mall, Stanford, California 94305–6072
Email:
peter.hammond@stanford.edu
Yeneng Sun
Affiliation:
Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543 – and – Department of Economics, National University of Singapore, 1 Arts Link, Singapore 117570
Email:
matsuny@nus.edu.sg
DOI:
http://dx.doi.org/10.1090/S0002993905080160
PII:
S 00029939(05)080160
Keywords:
Loeb product measures,
productmeasurable sets,
continuum of independent random variables,
joint measurability problem,
oneway Fubini property
Received by editor(s):
July 31, 2002
Received by editor(s) in revised form:
October 8, 2004
Published electronically:
July 18, 2005
Additional Notes:
Part of this work was done when the first author was visiting Singapore in November 1999 and when the second author was visiting Stanford in July 2002.
Communicated by:
Carl G. Jockusch, Jr.
Article copyright:
© Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
