The haar measure problem

Adam J. Przeździecki; Piotr Szewczak; Boaz Tsaban

doi:10.1090/proc/14221

The haar measure problem

Adam J. Przeździecki, Piotr Szewczak, Boaz Tsaban

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	1051-1057
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	147
Issue number	3
DOIs	https://doi.org/10.1090/proc/14221
State	Published - Mar 2019

Keywords

Baire property
Closed measure zero
Compact group
Haar measurable
Profinite group

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Access to Document

10.1090/proc/14221

https://www.ams.org/proc/2019-147-03/S0002-9939-2018-14221-5/S0002-9939-2018-14221-5.pdf

Cite this

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KW - Closed measure zero

KW - Compact group

KW - Haar measurable

KW - Profinite group

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The haar measure problem

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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