Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

On translations of subsets of the real line

Author(s): Jacek Cichon; Andrzej Jasinski; Anastasis Kamburelis; Przemyslaw Szczepaniak
Journal: Proc. Amer. Math. Soc. 130 (2002), 1833-1842.
MSC (2000): Primary 03E15; Secondary 28A05
Posted: October 17, 2001
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

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.

References:

[CP]
K. Ciesielski and J. Pawlikowski, A combinatorial core of the iterated perfect set model, preprint.

[J]
T. Jech, Set Theory, Academic Press, New York, 1978. MR 80a:03062

[K]
A. S. Kechris, Classical Descriptive Set Theory, Grad. Texts in Math. 156, Springer, 1995. MR 96e:03057

[L]
M. Laczkovich, Two constructions of Sierpinski and some cardinal invariants of ideals, Real Analysis Exchange 24 (1998/9), 663-676. MR 2000f:03148

[LM]
M. Laczkovich and A. W. Miller, Measurability of functions with approximately continuous vertical sections and measurable horizontal sections, Colloq. Math. 69 (1995), 299-308. MR 96k:28005

[M]
A. W. Miller, Infinite combinatorics and definability, Ann. Pure Appl. Logic 41 (1989), 179-203. MR 90b:03070

[M1]
J. Mycielski, Independent sets in topological algebras, Fund. Math. 55 (1964), 139-147. MR 30:3855

[M2]
J. Mycielski, Algebraic independence and measure, Fund. Math. 61 (1967), 165-169. MR 37:361

[Ox]
J. C. Oxtoby, Measure and category, Springer, Berlin, 1971. MR 52:14213

[S1]
W. Sierpinski, Sur les translation des ensembles lineares, Fund. Math. 19 (1932), 22-28.

[S2]
W. Sierpinski, Sur les translation des ensembles lineares, Fund. Math. 35 (1948), 159-164. MR 10:287d

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 03E15, 28A05

Retrieve articles in all Journals with MSC (2000): 03E15, 28A05

Additional Information:

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

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

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

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

DOI: 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
Posted: October 17, 2001
Communicated by: Alan Dow
Copyright of article: Copyright 2001, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google