4 papers
Convergence of martingales via enriched dagger categories
Paolo Perrone, Ruben Van Belle
We provide a categorical proof of convergence for martingales and backward martingales in mean, using enriched category theory. The enrichment we use is in topological spaces, with…
A categorical treatment of the Radon-Nikodym theorem and martingales
Ruben Van Belle
In this paper we will give a categorical proof of the Radon-Nikodym theorem. We will do this by describing the trivial version of the result on finite probability spaces as a natur…
A categorical proof of the Carathéodory extension theorem
Ruben Van Belle
The Carathéodory extension theorem is a fundamental result in measure theory. Often we do not know what a general measurable subset looks like. The Carathéodory extension theorem s…
Probability monads as codensity monads
Ruben Van Belle
We show from a categorical point of view that probability measures on certain measurable or topological spaces arise canonically as the extension of probability distributions on co…