The haar measure problem

Adam J. Przeździecki, Piotr Szewczak, Boaz Tsaban

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish
Pages (from-to)1051-1057
Number of pages7
JournalProceedings of the American Mathematical Society
Issue number3
StatePublished - Mar 2019

Bibliographical note

Publisher Copyright:
© 2018 American Mathematical Society.


  • Baire property
  • Closed measure zero
  • Compact group
  • Haar measurable
  • Profinite group


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