The Distribution Function of a Probability Measure on a Linearly Ordered Topological Space

Abstract

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.

Keywords

• probability
• measure
• σ-algebra
• Borel σ-algebra
• distribution function
• cumulative distribution function
• sample
• linearly ordered topological space