Economic Theory

, Volume 8, Issue 1, pp 41–50

A law of large numbers for large economies

  • Harald Uhlig
Research Articles

DOI: 10.1007/BF01212011

Cite this article as:
Uhlig, H. Econ Theory (1996) 8: 41. doi:10.1007/BF01212011

Summary

LetX(i),iε[0; 1] be a collection of identically distributed and pairwise uncorrelated random variables with common finite meanμ and variance σ2. This paper shows the law of large numbers, i.e. the fact that ∝01X(i)di=μ. 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.

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Harald Uhlig
    • 1
    • 2
  1. 1.CentERTilburg UniversityLE TilburgThe Netherlands
  2. 2.CEPRThe Netherlands