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

## Author Info

Listed author(s):
• 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.

To our knowledge, this item is not available for download. To find whether it is available, there are three options:
1. Check below under "Related research" 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.

## Bibliographic Info

Article provided by Springer & Society for the Advancement of Economic Theory (SAET) in its journal Economic Theory.

Volume (Year): 8 (1996)
Issue (Month): 1 ()
Pages: 41-50

as
in new window

 Handle: RePEc:spr:joecth:v:8:y:1996:i:1:p:41-50 Note: Received: June 10, 1994; revised version June 9th 1995 Contact details of provider: Web page: http://www.springer.com Order Information: Web: http://www.springer.com/economics/economic+theory/journal/199/PS2

## References

References listed on IDEAS
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.:

as
in new window

1. Vives, X. & Mas-Colell, A., 1989. "Implementation in economies with a Continuum of Agents," UFAE and IAE Working Papers 129.90, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
Full references (including those not matched with items on IDEAS)

## Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

## Corrections

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)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.