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arXiv · 2607.06201

On the independence of axioms for measures of non-compactness

Jerzy Grzybowski·Piotr Kasprzak·Piotr Maćkowiak
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Abstract

We investigate the independence of the axioms in the Bana\'s--Goebel approach to the theory of measures of non-compactness. We present a complete answer for four of the five axioms. For the remaining axiom, we provide a full solution in finite-dimensional spaces and a partial one in the infinite-dimensional case.

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Jerzy Grzybowski, Piotr Kasprzak, Piotr Maćkowiak. 2026-07-07. On the independence of axioms for measures of non-compactness. https://arxiv.org/abs/2607.06201

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