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Proceedings of the American Mathematical Society

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On the sum of two Borel sets


Authors: P. Erdős and A. H. Stone
Journal: Proc. Amer. Math. Soc. 25 (1970), 304-306
MSC: Primary 28.10; Secondary 54.00
DOI: https://doi.org/10.1090/S0002-9939-1970-0260958-1
Acknowledgment: Proc. Amer. Math. Soc. 29, no. 3 (1971), p. 628.
MathSciNet review: 0260958
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Abstract: It is shown that the linear sum of two Borel subsets of the real line need not be Borel, even if one of them is compact and the other is $ {G_\delta }$. This result is extended to a fairly wide class of connected topological groups.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0260958-1
Keywords: Borel set, analytic set, complete metric space, Cantor set, algebraically independent, connected topological group, absolute $ {G_\delta }$
Article copyright: © Copyright 1970 American Mathematical Society