Measures and dynamics on Noetherian spaces

TL;DR

This paper characterizes finite Borel measures on Noetherian spaces and explores their duality with function spaces, applying these insights to analyze the long-term behavior of continuous dynamical systems in such spaces.

Contribution

It provides an explicit description of measures on Noetherian spaces and links them to function spaces, advancing understanding of measure dynamics in these settings.

Findings

Finite Borel measures are explicitly characterized on Noetherian spaces.

Measures are shown to be dual to a specific space of functions.

Results are applied to study asymptotic behavior of dynamical systems.

Abstract

We give an explicit description of all finite Borel measures on Noetherian topological spaces X, and characterize them as objects dual to a space of functions on X. We use these results to study the asymptotic behavior of continuous dynamical systems on Noetherian spaces.