An old problem asks whether every compact group has a Haarnonmeasurable subgroup. A series of earlier results reduced 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.
|Number of pages||7|
|Journal||Proceedings of the American Mathematical Society|
|State||Published - Mar 2019|
Bibliographical notePublisher Copyright:
© 2018 American Mathematical Society.
- Baire property
- Closed measure zero
- Compact group
- Haar measurable
- Profinite group