Smoothing causal functions

TL;DR

This paper characterizes the set of causal functions approximable by smooth Lyapunov functions within the framework of closed cone fields, providing new insights into causality theory.

Contribution

It introduces a general framework for approximating causal functions by smooth Lyapunov functions in closed cone fields, advancing causality theory.

Findings

Identification of causal functions approximable by smooth Lyapunov functions

Implications for causality theory in closed cone fields

New theoretical results on the structure of causal functions

Abstract

We describe, in the general setting of closed cone fields, the set of causal functions which can be approximated by smooth Lyapunov. We derive several consequences on causality theory. Dans le contexte g\'en\'eral des champs de cones ferm\'es, on d\'ecrit l'ensemble des fonctions causales qui peuvent \^etre approch\'ees par des fonctions de Lyapunov lisses. On en d\'eduit quelques cons\'equence en th\'eorie de la causalit\'e.