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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Universally meager sets


Author: Piotr Zakrzewski
Journal: Proc. Amer. Math. Soc. 129 (2001), 1793-1798
MSC (1991): Primary 03E20, 54E52; Secondary 54G99, 28A05
Published electronically: November 2, 2000
MathSciNet review: 1814112
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Abstract:

We study category counterparts of the notion of a universal measure zero set of reals.

We say that a set $A\subseteq {\mathbb R}$ is universally meager if every Borel isomorphic image of $A$ is meager in ${\mathbb R}$. We give various equivalent definitions emphasizing analogies with the universally null sets of reals.

In particular, two problems emerging from an earlier work of Grzegorek are solved.


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Additional Information

Piotr Zakrzewski
Affiliation: Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland
Email: piotrzak@mimuw.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05726-9
PII: S 0002-9939(00)05726-9
Keywords: Measure and category, Borel sets, Baire property, $\sigma$-algebra, $\sigma$-ideal
Received by editor(s): March 23, 1999
Received by editor(s) in revised form: September 7, 1999
Published electronically: November 2, 2000
Additional Notes: The author was partially supported by KBN grant 2 P03A 047 09 and by the Alexander von Humboldt Foundation.
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2000 American Mathematical Society