Illinois Journal of Mathematics

Strong measure zero sets in Polish groups

Michael Hrušák and Jindřich Zapletal

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In the context of arbitrary Polish groups, we investigate the Galvin–Mycielski–Solovay characterization of strong measure zero sets as those sets for which a meager collection of right translates cannot cover the whole group.

Article information

Source
Illinois J. Math., Volume 60, Number 3-4 (2016), 751-760.

Dates
Received: 15 September 2016
Revised: 6 May 2017
First available in Project Euclid: 22 September 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1506067289

Digital Object Identifier
doi:10.1215/ijm/1506067289

Mathematical Reviews number (MathSciNet)
MR3707641

Zentralblatt MATH identifier
06790325

Subjects
Primary: 03E35: Consistency and independence results 22A05: Structure of general topological groups 20B35: Subgroups of symmetric groups

Citation

Hrušák, Michael; Zapletal, Jindřich. Strong measure zero sets in Polish groups. Illinois J. Math. 60 (2016), no. 3-4, 751--760. doi:10.1215/ijm/1506067289. https://projecteuclid.org/euclid.ijm/1506067289


Export citation

References

  • T. J. Carlson, Strong measure zero and strongly meager sets, Proc. Amer. Math. Soc. 118 (1993), 577–586.
  • D. H. Fremlin, Measure theory, vol. 5, Set-theoretic measure theory, 2008; available at http://www.essex.ac.uk/maths/people/fremlin/mt5.2008/mt5.2008.tar.gz.
  • F. Galvin, J. Mycielski and R. Solovay, Strong measure zero sets, Notices Amer. Math. Soc. 26: (1979), \bnumberA–280.
  • M. Hrušák, W. Wohofsky and O. Zindulka, Strong measure zero in separable metric spaces and Polish groups, Arch. Math. Logic 55 (2016), 105–131.
  • T. Jech, Set theory, Academic Press, San Diego, 1978.
  • M. Kysiak, On Erdős–Sierpiński duality between Lebesgue measure and Baire category, Ph.D. thesis, Warsaw University, 2000.
  • P. B. Larson, The stationary tower forcing, University Lecture Series, vol. 32, American Mathematical Society, Providence, RI, 2004. Notes from Woodin's lectures.
  • R. Laver, On the consistency of Borel's conjecture, Acta Math. 137 (1987), 151–169.