Antisymmetry of the stochastic order on all ordered topological spaces

TL;DR

This paper proves that the stochastic order of Radon probability measures on any ordered topological space is antisymmetric, providing a simple proof that generalizes previous special cases.

Contribution

It establishes the antisymmetry of stochastic order in all ordered topological spaces, extending known results with a straightforward proof.

Findings

Stochastic order is antisymmetric on all ordered topological spaces.

The proof is simple and elementary, applicable to general cases.

Generalizes previous results in specific 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.