The law of large numbers with a continuum of i.i.d. random variables
type: Item
instance of: scholarly article
title: The law of large numbers with a continuum of i.i.d. random variables
zbMATH Open document ID: 0569.60037
DOI: 10.1016/0022-0531(85)90059-6
author: Kenneth L. Judd
published in: Journal of Economic Theory
publication date: 1985-01-01T00:00:00Z
review text: There are two problems with the common argument that a continuum of independent and identically distributed random variables sum to a nonrandom quantity in ''large economies''. First, it may be unintelligible in that it may call for the measure of a nonmeasurable set. However, there is a probability measure, consistent with the finite-dimensional distributions, which assigns zero measure to the set of realizations having that difficulty. A second difficulty is that the ''law of large numbers'' may not hold even when there is no measurability problem.
Mathematics Subject Classification ID: 60F99
zbMATH DE Number: 3909441
zbMATH Keywords: law of large numbers
zbMATH Keywords: continuum of independent and identically distributed random variables
MaRDI profile type: Publication
full work available at URL: 0022-0531(85)90059-6
OpenAlex ID: W1980700045
cites work: Q4197800
cites work: Nonstandard Exchange Economies
cites work: Q5593890
description: scientific article; zbMATH DE number 3909441