Antisymmetry of the Stochastical Order on all Ordered Topological Spaces

Abstract

In this short note, we prove that the stochastic order of Radon probability measures on any ordered topological space is antisymmetric. This has been known before in various special cases. We give a simple and elementary proof of the general result.

Keywords

• stochastic order
• ordered metric spaces
• primary: 60e15
• secondary: 28c15