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Analytic subgroups of the reals


Author: Miklós Laczkovich
Journal: Proc. Amer. Math. Soc. 126 (1998), 1783-1790
MSC (1991): Primary 04A15
DOI: https://doi.org/10.1090/S0002-9939-98-04241-5
MathSciNet review: 1443837
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Abstract: We prove that every analytic proper subgroup of the reals can be covered by an $F_{\sigma }$ null set. We also construct a proper Borel subgroup $G$ of the reals that cannot be covered by countably many sets $A_{i}$ such that $A_{i} +A_{i}$ is nowhere dense for every $i.$


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Additional Information

Miklós Laczkovich
Affiliation: Department of Analysis, Eötvös Loránd University, Budapest, Muzeum krt. 6-8, Hungary 1088
Email: laczk@cs.elte.hu

DOI: https://doi.org/10.1090/S0002-9939-98-04241-5
Received by editor(s): February 20, 1996
Received by editor(s) in revised form: November 21, 1996
Additional Notes: This work was completed when the author had a visiting position at the Mathematical Institute of the Hungarian Academy of Sciences. Also supported by the Hungarian National Foundation for Scientific Research, Grant T016094.
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1998 American Mathematical Society

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