  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.
