Joint Measurability and the One-way Fubini Property for a Continuum of Independent Random Variables
April 2000 As is well known, a continuous parameter process with mutually independent random variables is not jointly measurable in the usual sense. This paper proposes using a natural ``one-way Fubini'' property that guarantees a unique meaningful solution to this joint measurability problem when the random variables are independent even in a very weak sense. In particular, if F is the smallest extension of the usual product sigma-algebra such that the process is measurable, then there is a unique probability measure v on F such that the integral of any v-integrable function is equal to a double integral evaluated in one particular order. Moreover, in general this measure cannot be further extended to satisfy a two-way Fubini property. However, the extended framework with the one-way Fubini property not only shares many desirable features previously demonstrated under the stronger two-way Fubini property, but also leads to a new characterization of the most basic probabilistic concept --- stochastic independence in terms of regular conditional distributions.
|Date of creation:||Apr 2000|
|Contact details of provider:|| Postal: Ralph Landau Economics Building, Stanford, CA 94305-6072|
Web page: http://www-econ.stanford.edu/econ/workp/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Douglas W. Diamond & Philip H. Dybvig, 2000.
"Bank runs, deposit insurance, and liquidity,"
Federal Reserve Bank of Minneapolis, issue Win, pages 14-23.
- Diamond, Douglas W & Dybvig, Philip H, 1983. "Bank Runs, Deposit Insurance, and Liquidity," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 401-419, June.
- Celentani, Marco & Pesendorfer, Wolfgang, 1996. "Reputation in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 70(1), pages 109-132, July.
- Marco Celentani & Wolfgang Pesendorfer, 1992. "Reputation in Dynamic Games," Discussion Papers 1009, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Anderson, Robert M., 1991. "Non-standard analysis with applications to economics," Handbook of Mathematical Economics,in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 39, pages 2145-2208 Elsevier.
- Edward J. Green, 1994. "Individual Level Randomness in a Nonatomic Population," GE, Growth, Math methods 9402001, EconWPA.
- Lucas, Robert Jr. & Prescott, Edward C., 1974. "Equilibrium search and unemployment," Journal of Economic Theory, Elsevier, vol. 7(2), pages 188-209, February. Full references (including those not matched with items on IDEAS)