Null-additive sets and packing measures

Ond{ř}ej Zindulka

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arXiv · 2610.05283

Null-additive sets and packing measures

Ond{ř}ej Zindulka

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Abstract

A separable metric space has strict measure zero if its packing measure induced by any gauge is zero. We provide a few characterizations of strict measure zero, look at cartesian products and prove that in every Polish locally compact group every set of strict measure zero is null-additive and that in the Cantor set, Euclidean spaces and tori the two notions are equivalent.

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Ond{ř}ej Zindulka. 2026-10-04. Null-additive sets and packing measures. https://arxiv.org/abs/2610.05283

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