Antisymmetry of the stochastic 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.

arXiv comment4 pages. v2: stronger result for all ordered topological spaces

References in corpus (1)

• Stochastic order on metric spaces and the ordered Kantorovich monad

Cited by in corpus (2)

• Stochastic order on metric spaces and the ordered Kantorovich monad
• Characterizing the asymptotic and catalytic stochastic orders on topological abelian groups