PreprintarXiv licencearXiv
Invariant means, coset correct means and the Hahn-Banach Theorem
Abstract
We show that, in ZF set theory, the existence of "coset correct means" on all groups is equivalent to the Hahn-Banach Theorem, as well as to the existence of invariant means on abelian groups.
Related
- Certifiably Correct Fréchet Means in Orbit Spaces
- H-Operator Approximation Spaces via Delayed Riesz Means and Quasi-Banach Moduli
- Spectral theorem for compact self-adjoint operators on smooth Banach spaces
- A Banach--Stone-like Theorem for Slowly Oscillating Functions
- A Hartman-Grobman theorem on Banach bundles
BibTeX
@misc{martino2026invariant,
title = {{Invariant means, coset correct means and the Hahn-Banach Theorem}},
author = {Armando Martino and Motiejus Valiunas},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38944},
eprint = {2610.38944},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38944},
}
RIS
TY - UNPB
TI - Invariant means, coset correct means and the Hahn-Banach Theorem
AU - Armando Martino
AU - Motiejus Valiunas
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38944
UR - https://arxiv.org/abs/2610.38944
AB - We show that, in ZF set theory, the existence of "coset correct means" on all groups is equivalent to the Hahn-Banach Theorem, as well as to the existence of invariant means on abelian groups.
ER -