The Haar measure problem
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- by Adam J. Przeździecki, Piotr Szewczak and Boaz Tsaban PDF
- Proc. Amer. Math. Soc. 147 (2019), 1051-1057 Request permission
Abstract:
An old problem asks whether every compact group has a Haar-nonmeasurable 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.References
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Additional Information
- Adam J. Przeździecki
- Affiliation: Warsaw University of Life Sciences—SGGW, Warsaw, Poland
- Email: adamp@mimuw.edu.pl
- Piotr Szewczak
- Affiliation: Faculty of Mathematics and Natural Science College of Sciences, Cardinal Stefan Wyszyński University in Warsaw, Warsaw, Poland — and — Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel
- MR Author ID: 922212
- Email: p.szewczak@wp.pl
- Boaz Tsaban
- Affiliation: Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel
- MR Author ID: 632515
- Email: tsaban@math.biu.ac.il
- Received by editor(s): September 7, 2017
- Received by editor(s) in revised form: September 8, 2017
- Published electronically: December 3, 2018
- Communicated by: Heike Mildenberger
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 1051-1057
- MSC (2010): Primary 28C10, 28A05, 22C05, 03E17
- DOI: https://doi.org/10.1090/proc/14221
- MathSciNet review: 3896055