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

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

2 Scopus citations

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

Bibliographical note

Publisher Copyright:
© 2018 American Mathematical Society.

Keywords

Baire property
Closed measure zero
Compact group
Haar measurable
Profinite group

Access to Document

10.1090/proc/14221

Cite this

@article{8e0a8d41e5eb4d1ca8b5db7fae20b689,

title = "The haar measure problem",

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.",

keywords = "Baire property, Closed measure zero, Compact group, Haar measurable, Profinite group",

author = "Prze{\'z}dziecki, {Adam J.} and Piotr Szewczak and Boaz Tsaban",

note = "Publisher Copyright: {\textcopyright} 2018 American Mathematical Society.",

year = "2019",

month = mar,

doi = "10.1090/proc/14221",

language = "אנגלית",

volume = "147",

pages = "1051--1057",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "3",

}

TY - JOUR

T1 - The haar measure problem

AU - Przeździecki, Adam J.

AU - Szewczak, Piotr

AU - Tsaban, Boaz

PY - 2019/3

Y1 - 2019/3

N2 - 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.

AB - 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.

KW - Baire property

KW - Closed measure zero

KW - Compact group

KW - Haar measurable

KW - Profinite group

UR - http://www.scopus.com/inward/record.url?scp=85065198559&partnerID=8YFLogxK

U2 - 10.1090/proc/14221

DO - 10.1090/proc/14221

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85065198559

SN - 0002-9939

VL - 147

SP - 1051

EP - 1057

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 3

ER -

The haar measure problem

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this