The Haar Measure Problem
General Topology
2018-05-14 v3 Functional Analysis
Logic
Abstract
An old problem asks whether every compact group has a Haar-nonmeasurable subgroup. A series of earlier results reduce the problem to infinite metrizable profinite groups. We provide a positive answer, assuming a weak, potentially provable, consequence of the Continuum Hypothesis. We also establish the dual, Baire category analogue of this result.
Cite
@article{arxiv.1709.02312,
title = {The Haar Measure Problem},
author = {Adam J. Przeździecki and Piotr Szewczak and Boaz Tsaban},
journal= {arXiv preprint arXiv:1709.02312},
year = {2018}
}
Comments
To appear in Proceedings of the AMS