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arXiv · 2604.19617

A truncation criterion for compactness in asymptotic $L_p$ spaces

Nuno J. Alves
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Abstract

We prove a compactness criterion for asymptotic $L_p$ spaces over arbitrary measure spaces. Total boundedness is characterized by almost equiboundedness together with total boundedness in $L_p$ of all truncations. As a consequence, we obtain a simpler proof of the Kolmogorov--Riesz compactness theorem for asymptotic $L_p$ spaces on $\mathbb R^n$.

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Nuno J. Alves. 2026-04-21. A truncation criterion for compactness in asymptotic $L_p$ spaces. https://arxiv.org/abs/2604.19617

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