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Subadditive bijections on the positive reals
Abstract
We show that there exists a subadditive bijection f:(0,∞)→(0,∞) such that liminfx→ 0f(x)=0 and limsupx→ 0f(x)=1. This answers a question by Matkowski and Swiatkowski in [Proc. Amer. Math. Soc. 119 (1993), 187--197].
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BibTeX
@misc{leonetti2026subadditive,
title = {{Subadditive bijections on the positive reals}},
author = {Paolo Leonetti},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35851},
eprint = {2609.35851},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35851},
}
RIS
TY - UNPB
TI - Subadditive bijections on the positive reals
AU - Paolo Leonetti
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.35851
UR - https://arxiv.org/abs/2609.35851
AB - We show that there exists a subadditive bijection f:(0,∞)→(0,∞) such that liminf_x→ 0f(x)=0 and limsup_x→ 0f(x)=1. This answers a question by Matkowski and Swiatkowski in [Proc. Amer. Math. Soc. 119 (1993), 187--197].
ER -