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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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