# A law of large numbers for large economies (*)

## Author

Listed:
• Harald Uhlig

(Center, Tilburg University, Postbus 90153, 5000 LE Tilburg, THE NETHERLANDS, and CEPR)

## Abstract

Let $X(i),$$i\in [0;1]$ be a collection of identically distributed and pairwise uncorrelated random variables with common finite mean µ and variance $\sigma^{2}.$ This paper shows the law of large numbers, i.e. the fact that $\int^{1}_{0}X(i)di=\mu .$ It does so by interpreting the integral as a Pettis-integral. Studying Riemann sums, the paper first provides a simple proof involving no more than the calculation of variances, and demonstrates, that the measurability problem pointed out by Judd (1985) is avoided by requiring convergence in mean square rather than convergence almost everywhere. We raise the issue of when a random continuum economy is a good abstraction for a large finite economy and give an example in which it is not.

## Suggested Citation

• Harald Uhlig, 1996. "A law of large numbers for large economies (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 41-50.
• Handle: RePEc:spr:joecth:v:8:y:1996:i:1:p:41-50 Note: Received: June 10, 1994; revised version June 9th 1995
as

To our knowledge, this item is not available for download. To find whether it is available, there are three options:
1. Check below whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.

## References listed on IDEAS

as
1. Andreu Mas-Colell & Xavier Vives, 1993. "Implementation in Economies with a Continuum of Agents," Review of Economic Studies, Oxford University Press, vol. 60(3), pages 613-629.
Full references (including those not matched with items on IDEAS)

## Corrections

All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joecth:v:8:y:1996:i:1:p:41-50. 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: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: http://www.springer.com .

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.