Individual-level randomness in a nonatomic population

TL;DR

This paper constructs a family of i.i.d. random vectors indexed by a nonatomic measure space, ensuring samples exactly match their distribution and exhibit homogeneity, which is useful for economic applications.

Contribution

It introduces a novel construction of i.i.d. random vectors indexed by a nonatomic space with exact distributional properties and homogeneity.

Findings

Samples have a.s. the distribution they are drawn from

Any positive measure subspace inherits the same property

Construction supports applications in economics

Abstract

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) a sample is a measurable function from the index space, and (b) an idealization of the Glivenko-Cantelli theorem holds exactly with respect to the measure on that space. That is, samples possess a.s. the distribution from which they are drawn. Moreover, any subspace of the index space with positive measure inherits the same property. This homogeneity property is important for applications of the construction in economics.