Measurable order and simulation

Abstract

In this article is proposed a method for simulating random objects in a sample space Ω provided with a probability measure, a total order and general conditions, such as the fact that for all ω 0 ∈ Ω the set {ω ∈ Ω: ω ω 0 } is measurable, the order topology relative to is first countable, and a completion of Ω relative to the order is also first countable.