A Stone-Weierstrass approximation theorem for monotone functions
Functional Analysis
2025-12-04 v1 Mathematical Physics
General Topology
math.MP
Abstract
We present an approximation theorem for continuous non-decreasing functions on compact preordered spaces, leading to an algebraic characterization of their corresponding function spaces. As an application, we prove that the family of positive non-decreasing rational functions with non-negative coefficients can uniformly approximate all continuous non-decreasing functions on compact intervals. An explicit approximation formula of this type is provided.
Cite
@article{arxiv.2512.03633,
title = {A Stone-Weierstrass approximation theorem for monotone functions},
author = {Ettore Minguzzi},
journal= {arXiv preprint arXiv:2512.03633},
year = {2025}
}
Comments
20 pages