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

 

On translations of subsets of the real line


Authors: Jacek Cichon, Andrzej Jasinski, Anastasis Kamburelis and Przemyslaw Szczepaniak
Journal: Proc. Amer. Math. Soc. 130 (2002), 1833-1842
MSC (2000): Primary 03E15; Secondary 28A05
Published electronically: October 17, 2001
MathSciNet review: 1887032
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Abstract: In this paper we discuss various questions connected with translations of subsets of the real line. Most of these questions originate from W. Sierpinski. We discuss the number of translations a single subset of the reals may have. Later we discuss almost invariant subsets of Abelian groups.


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Additional Information

Jacek Cichon
Affiliation: Institute of Mathematics, Wrocław University, Pl. grunwaldzki 2/4, 50–384 Wrocław, Poland

Andrzej Jasinski
Affiliation: Institute of Mathematics, Wrocław University, Pl. grunwaldzki 2/4, 50–384 Wrocław, Poland

Anastasis Kamburelis
Affiliation: Institute of Mathematics, Wrocław University, Pl. grunwaldzki 2/4, 50–384 Wrocław, Poland
Email: akamb@math.uni.wroc.pl

Przemyslaw Szczepaniak
Affiliation: Institute of Mathematics, Wrocław University, Pl. grunwaldzki 2/4, 50–384 Wrocław, Poland

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06224-4
PII: S 0002-9939(01)06224-4
Keywords: Lebesgue measure, Baire property, almost invariant sets
Received by editor(s): July 6, 2000
Received by editor(s) in revised form: December 8, 2000
Published electronically: October 17, 2001
Communicated by: Alan Dow
Article copyright: © Copyright 2001 American Mathematical Society