%0 Journal Article %T The Distribution Function of a Probability Measure on a Linearly Ordered Topological Space %J Mathematics | An Open Access Journal from MDPI %D 2019 %R https://doi.org/10.3390/math7090864 %X In this paper, we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case. Moreover, we define its pseudo-inverse and study its properties. Those properties will allow us to generate samples of a distribution and give us the chance to calculate integrals with respect to the related probability measure. View Full-Tex %U https://www.mdpi.com/2227-7390/7/9/864