Proceedings of the American Mathematical Society

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

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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 03E20, 54E52, 54G99, 28A05

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

DOI: 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
Posted: 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.
Copyright of article: Copyright 2000, American Mathematical Society

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