PreprintarXiv licencearXiv
Null-additive sets and packing measures
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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BibTeX
@misc{zindulka2026nulladditive,
title = {{Null-additive sets and packing measures}},
author = {Ondřej Zindulka},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05283},
eprint = {2610.05283},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05283},
}
RIS
TY - UNPB
TI - Null-additive sets and packing measures
AU - Ond{ř}ej Zindulka
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05283
UR - https://arxiv.org/abs/2610.05283
AB - 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.
ER -