The Haar Measure Problem

2017/09/07 by Przeździecki, Adam J., Szewczak, Piotr, Tsaban, Boaz
#FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #Logic (math.LO)

paper · doi:10.48550/arxiv.1709.02312

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.

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• Haar measure for non-Hausdorff locally compact groups
• Nonmeasurable subgroups of compact groups
• Haar Measures
• Every compact group can have a non-measurable subgroup
• On a Cardinal Invariant Related to the Haar Measure Problem