Rational probability measures

Abstract

In this paper we introduce the concept of rational probability measures. These are probability measures that map every Borel event to a rational number. We show that a rational probability measure has a nite support. As a consequence we prove a new version of Kolmogorov extension theorem. In the second part of the paper we dene N-rational probability measures as the set of probability measures that map every Borel event to a rational number with denominator in N N. We show that for every nite N N, the set of N-rational probability measures is closed in the space of Borel probability measures. The latter is not true when N is innite.