Individual Level Randomness in a Nonatomic Population
This paper provides a construction of an uncountable family of i.i.d. random vectors, indexed by the points of a nonatomic measure space, such that (a) samples are measurable functions from the index space, and (b) an exact analogue of the Glivenko-Cantelli theorem holds with respect to the measure on that space. That is, a sample possesses a.s. the same distribution as that of the random vectors from which it is drawn. Moreover, any subspace of the index space with positive measure inherits the same property. This homogeneity property is important for an application of the construction to mathematical economics.
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.:
- A. Meltzer & Peter Ordeshook & Thomas Romer, 1982. "Introduction," Public Choice, Springer, vol. 39(1), pages 1-3, January.
- Harald Uhlig, 1996.
"A law of large numbers for large economies (*),"
Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 41-50.
- Judd, Kenneth L., 1985. "The law of large numbers with a continuum of IID random variables," Journal of Economic Theory, Elsevier, vol. 35(1), pages 19-25, February.
- Feldman, Mark & Gilles, Christian, 1985. "An expository note on individual risk without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 35(1), pages 26-32, February.
When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpge:9402001. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA)
If references are entirely missing, you can add them using this form.