Every compact group can have a non-measurable subgroup

2015/03/04 by Brian, W. R., Mislove, M. W.
#FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1503.01385

Abstract

We show that it is consistent with ZFC that every compact group has a non-Haar-measurable subgroup. In addition, we demonstrate a natural construction, and we conjecture that this construction always produces a non-measurable subgroup of a given compact group. We prove that this is so in the Abelian case.

Related

• Nonmeasurable subgroups of compact groups
• The Haar Measure Problem
• Haar measure for non-Hausdorff locally compact groups
• Answer to a question of Rosłanowski and Shelah
• Products of finite groups and nonmeasurable subgroups