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arXiv · 2512.03633

A Stone-Weierstrass approximation theorem for monotone functions

Ettore Minguzzi
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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.

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BibTeXRIS

Ettore Minguzzi. 2025-12-03. A Stone-Weierstrass approximation theorem for monotone functions. https://arxiv.org/abs/2512.03633

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